Measurement. Chapter. What you will learn

Chpter 11 Mesurement Wht you will lern 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 11.10 Mesurement systems Using nd onverting metri lengths Perimeter Ares nd retngles Are of tringle Are of prllelogrm Are of omposite shpes Volume of retngulr prisms Cpity Mss nd temperture Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty. Cmridge University Press

561 Ntionl urriulum MEASUREMENT AND GEOMETRY Using units of mesurement Estlish the formuls for res of retngles, tringles nd prllelogrms nd use these in prolem solving Clulte volumes of retngulr prisms Shpe Drw different views of prisms nd solids formed from omintions of prisms Mesurement everywhere Imgine trying to desrie fts out the world round us without using ny form of mesurement. We use units of length to desrie distne nd degrees Celsius ( C) to desrie temperture. Other units re used for Are, Volume, Time, Cpity nd Mss. Here re some exmples of fts tht use different units of mesurement. The Eiffel Tower in Frne is pinted with 50 tonnes of pint every 7 yers. The Gret Wll of Chin is out 2400 km long. The Gret Pyrmid of Giz ws uilt round 2500 BCE nd inludes out 2 300 000 loks of stone, eh weighing out 2500 kg. The world s smllest ountry is Vtin City in Rome, with n re of 0.44 km2. The highest temperture during the dy on Mrs is out 25 C. The distne etween the orits of Mrs nd the Erth round the Sun is out 78 000 000 km. The volume of wter in Sydney Hrour is out 500 giglitres or five hundred thousnd million litres or 0.5 km3. Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty. Cmridge University Press

562 Chpter 11 Mesurement Pre-test 1 Mesure the length of these lines. 2 Arrnge these units from smllest to lrgest. entimetre (m), kilometre (km), metre (m), millimetre (mm) grm (g), kilogrm (kg), milligrm (mg), tonne (t) hour (h), yer, seond (s), dy, minute (min) 3 For eh of the following, find how mny: millimetres re in entimetre entimetres re in metre grms re in kilogrm d seonds re in minute e minutes re in n hour f millilitres re in litre 4 Clulte the nswer to eh of the following. 2 1000 200 100 56 000 1000 d 2.5 1000 e 3 60 f 2 60 60 g 1400 1000 h 27 1000 5 Find the totl distne round these shpes. 13 m 12 m 8 m 22 m 13 m 7 m 7 m 6 How mny unit squres mke up the re of these shpes? 7 How mny unit ues mke up the volume of these solids? 8 Give the most pproprite unit (e.g. metres) for mesuring eh of the following. distne etween two towns your weight length of shool lesson d width of lrge plte Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 563 11.1 Mesurement systems From out 3000 BCE unit of mesure lled the uit ws used in nient Egypt to mesure lengths. It is known tht the uit, whih is the length of n rm from the elow to the end of the middle finger, ws used to mesure the depth of the Nile River in flood. Other unit mesures sed on the humn ody were lso used. Some inlude the digit (width of Royl Cuits 1/3 1/4 1/2 1/2 1 1 1 Egyptins used their rms nd hnds to mesure different units. finger), plm (width of four fingers) nd spn (distne from the tip of the thum to the tip of the little finger in n outstrethed hnd). Beuse eh individul s rm length nd finger width is different, there ws need to develop stndrd unit of length. The Egyptins defined stndrd royl uit (out 524 mm), nd this ws represented s stone rod. From this uit the following divisions were mde: 28 digits in uit, 4 digits in plm nd 14 digits in spn. Mny of these units of mesurement were dpted nd developed y the Bylonins, Greeks, Romns, English nd Frenh over mny enturies. The English imperil system, whih ws dpted from the Romn nd Greek systems, is ommonly used in the United Kingdom nd the United Sttes tody, nd ws used in Austrli until the 1970s. Mny people tody still prefer to desrie lengths nd other mesures using Imperil units, suh s the inh nd mile. The metri system ws developed in Frne in the 1790s nd is the universlly epted system tody. The word metri omes from the Greek word metron, mening mesure. It is deiml system where length mesures re sed on the unit lled the metre. The definition of the metre hs hnged over time. Originlly it ws proposed to e the length of pendulum tht ets t rte of one per seond. It ws lter defined s 1/10 000 000 of the distne from the North Pole to the equtor on line on the Erth s surfe pssing through Pris. In 1960, metre eme 1 650 763.73 wve lengths of the spetrum of the krypton-86 tom in vuum. In 1983, the metre ws defined s the distne tht light trvels in 1/299 792 458 seonds inside vuum. Let s strt: Egyptin trder Imgine you re in nient Egypt nd you re trding goods t mrket. You use the Egyptin units: digit (width of finger), plm (width of four fingers) nd spn (distne from the top of the thum to the tip of the little finger in n outstrethed hnd). Use ruler to find the metri equivlent of your digit, plm nd spn. Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

564 Chpter 11 Mesurement You purhse wd of ppyrus pper tht is 1 digit thik. Whih students in the lss would get the lest pper if they used their own finger width? You purhse owl of grin 1 spn deep. Whih student in the lss gets the most grin? You purhse 5 uits of loth. Whih student gets the most loth? Key ides Anient mesurement systems tht developed from out 3000 BCE inlude the Egyptin, Bylonin, Greek nd Romn systems. The metri system is the ommonly used system tody. Romn system 1 foot = 12 inhes = 16 digits = 4 plms 1 uit = 6 plms 1 pe (doule step) = 5 feet 1 mile = 1000 pes imperil system 1 foot = 12 inhes (1 inh is out 2.5 m) 1 yrd = 3 feet (1 yrd is out 91.5 m) 1 rod = 16.5 feet 1 hin = 22 yrds 1 furlong = 40 rods 1 mile = 8 furlongs = 1760 yrds (1 mile is out 1.6 km) metri system 1 entimetre (m) = 10 millimetres (mm) 1 metre (m) = 100 entimetres (m) 1 kilometre (km) = 1000 metres (m) Exmple 1 Using mesurement systems How mny feet re there in 1 mile, using the Romn mesuring system? How mny inhes re there in 3 yrds, using the imperil system? Solution Explntion 1 mile = 1000 pes = 5000 feet There re 1000 pes in Romn mile nd 5 feet in pe. 3 yrds = 9 feet = 108 inhes There re 3 feet in n imperil yrd nd 12 inhes in foot. Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 565 Exmple 2 Choosing metri lengths Whih metri unit would e the most pproprite for mesuring these lengths? width of lrge room thikness of glss in window Solution Explntion metres (m) Using mm or m would give very lrge numer, nd using km would give numer tht is very smll. millimetres (mm) The thikness of glss is likely to e round 5 mm. Exerise 11A Exmple 1 1 Complete these numer sentenes. Romn system i 1 = 12 inhes = 16 = plms ii 1 = 1000 pes imperil system i 1 foot = 12 ii 3 = 1 yrd iii = 1760 yrds metri system i 1 m = m ii 1 m = mm iii km = 1000 m 2 List the units of length (e.g. uit), from smllest to lrgest, ommonly used in the Romn system. 3 List the units of length (e.g. inh), from smllest to lrgest, ommonly used in the imperil system. 4 List the units of length (e.g. entimetre), from smllest to lrgest, ommonly used in the metri system. 5 Use the Romn system to stte how mny: feet re in 1 pe feet re in 1 mile plms re in 1 foot d plms re in 1 pe e digits re in 1 foot f digits re in 1 pe Flueny Understnding Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

566 Chpter 11 Mesurement 6 Use the imperil system to stte how mny: inhes re in 1 foot feet re in 1 yrd inhes re in 1 yrd d yrds re in 1 mile e yrds re in 1 hin f rods re in 1 furlong Flueny 7 Use the metri system to stte how mny: millimetres re in 1 entimetre entimetres re in 1 metre metres re in 1 kilometre d millimetres re in 1 metre e entimetres re in 1 kilometre f millimetres re in 1 kilometre Exmple 2 8 Whih metri unit would e the most pproprite for mesuring the following? the distne etween two towns width of smll drill it height of flg pole d length of grden hose e width of smll desk f distne ross ity A drill it 9 Choose whih metri unit would e the most suitle for mesuring the length indited in these photos. d e f Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 567 10 A Romn offers you either 12 plms or 1 pe of loth. Whih option gives you the most loth? 11 The Romn rmy mrhes 5 Romn miles to the next post. How mny pes is the journey? 12 An English riketer runs 1 hin for eh run mde. How mny yrds will he run if he mkes 20 runs? Prolem-solving 13 Here is the length of 1 mm nd 1 m. Use these digrms s guide to estimte the length of these lines. d e 1 mm 1 m 14 Estimte the length of eh line or urve, in entimetres. 15 Complete these tles. metri imperil Resoning mm m m km mm 1 1 10 m 10 1 m 1000 1 km 1 inh feet yrd mile inh 1 1 36 feet 12 1 yrd 1 mile 1760 1 Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

568 Chpter 11 Mesurement Romn digit plm feet pe mile 1 digit 1 16 plm 4 1 feet 1 pe 1 mile 1 Resoning 16 Why would it e more diffiult to inlude the imperil units of hins nd rods in the tle in Question 15? 17 Generlly speking, why is the metri system esier to use thn either the imperil or Romn systems? Enrihment: Wlking pes 18 The Romn pe involves 2 steps, nd 1000 of these pes mke up Romn mile. These units would hve een used to estimte distnes for the Romn rmies tht spred throughout muh of the world during tht time. Estimte how mny pes (i.e. doule steps) you would tke in 1 kilometre (1000). Clulte how mny pes you would tke to over 1 kilometre. If eh pe tkes 1 seond, find how long it would tke to wlk from Sydney to Melourne (out 900 km) non-stop. Convert your nswer to numer of hours. Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 569 11.2 Using nd onverting metri lengths To void the use of very lrge nd very smll numers, n pproprite unit is often hosen to mesure length or distne. It my lso e neessry to onvert units of length. For exmple, 150 piees of timer, eh mesured in entimetres, my need to e ommunited s totl length using metres. Another exmple might e tht 5 millimetres is to e ut from length of timer 1.4 metres long euse it is is too wide to fit door opening tht is 139.5 entimetres wide. Let s strt: How good is your estimte? In less thn 3 seonds, guess the length of your desk, in entimetres. Now use ruler to find the tul length in entimetres. Convert your nswer to millimetres nd metres. If you lined up ll the lss desks end to end, how mny desks would e needed to reh 1 kilometre? Explin how you got your nswer. A rpenter my need to mesure lengths of wood in metres, entimetres nd millimetres. The metre (m) is the si metri unit of length. 1 km = 1000 m 1 m = 100 m 1000 100 1 m = 10 mm km m 1000 100 10 Conversion When onverting to smller unit, multiply y power of 10 (i.e. 10, 100, 1000). A smller unit mens you need more of them, so it mkes sense tht you multiply. When onverting to lrger unit, divide y power of 10 (i.e. 10, 100, 1000). A lrger unit mens you need less of them, so it mkes sense tht you divide. m 10 mm Key ides When reding sles, e sure out wht units re showing on the sle. This sle shows 36 mm. mm m 1 2 3 4 Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

570 Chpter 11 Mesurement Exmple 3 Converting metri units of length Convert to the units given in rkets. 3 m (m) 25 600 m (km) Solution Explntion 3 m = 3 100 m = 300 m 1 m = 100 m Multiply sine you re onverting to smller unit. 25 600 m = 25 600 100 000 = 0.256 km There re 100 m in 1 m nd 1000 m in 1 km nd 100 1000 = 100 000. Exmple 4 Reding length sles Red the sles on these rulers to mesure the mrked length. 1 m 2 m 3 m 5 m 6 m 7 m Solution Explntion 25 mm 2.5 m is lso urte. 70 m Eh division is 1 of metre, whih is 10 m. 10 Exerise 11B 1 Write down the missing numer or word in these sentenes. When onverting from metres to entimetres, you multiply y. When onverting from metres to kilometres, you divide y. When onverting from entimetres to metres, you y 100. d When onverting from kilometres to metres, you y 1000. e When onverting to smller unit, you. f When onverting to lrger unit, you. Understnding 2 Clulte eh of the following. 100 10 10 100 100 1000 d 10 100 1000 3 When multiplying y power of 10, in whih diretion does the deiml point move left or right? When dividing y power of 10, in whih diretion does the deiml point move left or right? Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 571 Exmple 3 Exmple 3 Exmple 4 4 Convert these mesurements to the units shown in rkets. 5 m (mm) 2 m (m) 3.5 km (m) d 26.1 m (m) e 40 mm (m) f 500 m (m) g 4200 m (km) h 472 mm (m) i 6.84 m (m) j 0.02 km (m) k 9261 mm (m) l 4230 m (km) 5 Add these lengths together nd give the result in the units shown in rkets. 2 m nd 5 mm (m) 8 m nd 2 mm (mm) 2 m nd 50 m (m) d 7 m nd 30 m (m) e 6 km nd 200 m (m) f 25 km nd 732 m (km) 6 Convert to the units shown in the rkets. 3 m (mm) 6 km (m) 2.4 m (mm) d 0.04 km (m) e 47 000 m (km) f 913 000 mm (m) g 216 000 mm (km) h 0.5 mm (m) 7 These rulers show entimetres with millimetre divisions. Red the sle to mesure the mrked length. Flueny 0 1 2 0 1 2 3 4 5 d 0 1 2 0 1 2 3 e f 0 1 2 3 4 0 1 2 3 4 5 g h 0 1 2 3 0 1 2 3 4 8 Red the sle on these tpe mesures. Be reful with the units shown! 0 m 1 2 3 11 12 13 km 9 Use sutrtion to find the differene etween the mesurements, nd give your nswer with the units shown in rkets. 9 km, 500 m (km) 3.5 m, 40 m (m) 0.2 m, 10 mm (m) Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

572 Chpter 11 Mesurement 10 Arrnge these mesurements from smllest to lrgest. 38 m, 540 mm, 0.5 m 0.02 km, 25 m, 160 m, 2100 mm 0.003 km, 20 m, 3.1 m, 142 mm d 0.001 km, 0.1 m, 1000 m, 10 mm 11 Joe widens 1.2 m doorwy y 50 mm. Wht is the new width of the doorwy, in entimetres? 12 Three onstrution engineers individully hve plns to uild the world s next tllest tower. The Titn tower is to e 1.12 km tll, the Gign tower is to e 109 500 m tll nd the Bign tower is to e 1210 m tll. Whih tower will e the tllest? 13 Steel hin osts $8.20 per metre. How muh does is ost to uy hin of the following lengths? 1 km 80 m 50 mm 14 A house is 25 metres from liff ove the se. The liff is eroding t rte of 40 mm per yer. How mny yers will pss efore the house strts to fll into the se? 15 Mount Everest is moving with the Indo-Austrlin plte t rte of out 10 m per yer. How mny yers will it tke to move 5 km? 16 A rem of 500 sheets of pper is 4 m thik. How thik is 1 sheet of pper, in millimetres? 17 A snil slithers 2 mm every 5 seonds. How long will it tke to slither 1 m? Prolem-solving 18 Copy this hrt nd fill in the missing informtion. 100 19 Mny trdespeople mesure nd ommunite with millimetres, even for long mesurements like timer ems or pipes. Cn you explin why this might e the se? km m m mm 10 Resoning Enrihment: Very long nd short lengths 20 When 1 metre is divided into 1 million prts, eh prt is lled mirometre (µm). At the other end of the spetrum, light yer is used to desrie lrge distnes in spe. Stte how mny mirometres there re in: i 1 m ii 1 m iii 1 mm iv 1 km A virus ell is 0.000 312 mm wide. How mny mirometres is this? Reserh the length lled the light yer. Explin wht it is nd give exmples of distnes using light yers, suh s to the nerest str other thn the Sun. Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 573 11.3 Perimeter The distne round the outside of 2-dimensionl shpe is lled the perimeter. The word perimeter omes from the Greek words peri, mening round, nd metron, mening mesure. We ssoite perimeter with the outside of ll sorts of regions nd ojets, like the length of fening surrounding lok of lnd or the length of timer required to frme piture. This fene mrks the perimeter (i.e. the distne round the outside) of pddok. Let s strt: Is there enough informtion? This digrm, whih is not drwn to sle, inludes only 90 ngles nd only one side length is given. Disuss if there is enough informtion given in the digrm to find the perimeter of the shpe. Wht dditionl informtion, if ny, is required? 10 m Perimeter, sometimes denoted s P, is the distne round the outside of 2-dimensionl shpe. Sides with the sme mrkings re of equl length. The unknown lengths of some sides n sometimes e determined y onsidering the given lengths of other sides. 2.8 m 4.1 m 1.6 m P = 1.6 + 1.6 + 2.8 + 4.1 = 10.1 m Key ides Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

574 Chpter 11 Mesurement Exmple 5 Finding the perimeter Find the perimeter of eh of these shpes. 3 m 3 m 5 m 6 m 5 m 2 m Solution Perimeter = 2 5 + 3 = 13 m Explntion There re two equl lengths of 5 m nd one length of 3 m. Perimeter = 2 6 + 2 8 = 28 m 3 m 6 2 = 4 m 6 m 5 m 3 + 5 = 8m 2 m Exerise 11C 1 These shpes re drwn on 1 m grids. Give the perimeter of eh. Understnding 2 Use ruler to mesure the lengths of the sides of these shpes, nd then find the perimeter. d Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 575 Exmple 5 3 Find the perimeter of these shpes. (Digrms re not drwn to sle.) 3 m 5 m 8 m 6 m 7 m 5 m 10 m 8 m Flueny d 1 m 10 km 0.2 m 5 km e f 10 m 2.5 m 6 m Exmple 5 4 Find the perimeter of these shpes. All orner ngles re 90. 4 m 2 m 5 m 10 m 7 m 8 m 5 m 4 m 6 km 3 km 9 km 5 A squre hs side length of 2.1 m. Find its perimeter. A retngle hs length of 4.8 m nd width of 2.2 m. Find its perimeter. An equilterl tringle hs ll sides the sme length. If eh side is 15.5 mm, find its perimeter. Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

576 Chpter 11 Mesurement 6 A grzing pddok is to e fened on ll sides. It is retngulr in shpe, with length of 242 m nd width of 186 m. If fening osts $25 per metre, find the ost of fening required. 7 A grss tennis ourt is lined with hlk. All the mesurements re shown in the digrm nd given in feet. Find the totl numer of feet of hlk required to do ll the lines of the given tennis ourt. There re 0.305 metres in 1 foot. Convert your nswer to prt to metres. 36 feet 21 feet 39 feet 27 feet Prolem-solving 8 Only some side lengths re shown for these shpes. Find the perimeter. 20 mm 4 m 15 mm 10 m 18 m 9 Find the perimeter of eh of these shpes. Give your nswers in entimetres. 271 mm 430 mm 7.1 m 168 mm 0.38 m 1.04 m 10 A squre pddok hs 100 eqully-sped posts tht re 4 metres prt, inluding one in eh orner. Wht is the perimeter of the pddok? 11 The perimeter of eh shpe is given. Find the missing length of eh. 4 m 2 m?? P = 11 m P = 20 m 12 km P = 38 km 12 A retngle hs perimeter of 16 m. Using only whole numers for the length nd width, how mny different retngles n e drwn? Do not ount rottions of the sme retngle.? Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 577 13 Write n lgeri rule (e.g. P = 2 + ) to desrie the perimeter of eh shpe. Resoning d e f 14 Write n lgeri rule for the perimeter of eh given shpe. 15 A squre hs perimeter P. Write n expression for its side length. A retngle hs perimeter P nd width. Write n expression for its length. Enrihment: Piture frmes 16 The mount of timer used to frme piture depends on the outside lengths of the overll frme. These re then ut t 45 to mke the frme. A squre pinting of side length 30 m is to e frmed with timer of width 5 m. Find the totl length of timer required for the jo. A retngulr photo with dimensions 50 m y 30 m is frmed with timer of width 7 m. Find the totl length of timer required to omplete the jo. Kimerley uses 2 m of timer of width 5 m to omplete squre piture frme. Wht is the side length of the piture? 30 m 30 m 5 m d A squre piee of emroidery hs side length m nd is frmed y timer of width 4 m. Write n expression for the totl mount of timer used. Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

578 Chpter 11 Mesurement 11.4 Ares nd retngles Are is mesured in squre units. It is often referred to s the mount of spe ontined inside flt (i.e. plne) shpe; however, urved 3-dimensionl (3D) solids lso hve surfe res. The mount of pint needed to pint house nd the mount of hemil needed to spry pddok re exmples of when re would e onsidered. Let s strt: The 12 m 2 retngle The greter the re of the pddok, the more hemils the plne needs to rry. A retngle hs n re of 12 squre entimetres (12 m 2 ). Drw exmples of retngles tht hve this re, showing the length nd width mesurements. How mny different retngles with whole numer dimensions re possile? How mny different retngles re possile if there is no restrition on the type of numers llowed to e used for length nd width? Key ides The metri units of re inlude: 1 squre millimetre (1 mm ) 1 squre entimetre (1 m ) 1 mm 1 mm 1 m 1 m 1 squre metre (1 m 2 ) 1 m (Not drwn to sle.) 1 m 1 squre kilometre (1 km 2 ) 1 km (Not drwn to sle.) 1 km 1 hetre (1 h) (10 000 m 2 ) 100 m (Not drwn to sle.) 100 m Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 579 The re of retngle is given y the numer of rows multiplied y the numer of olumns. Written s formul, this looks like: A = l w. This lso works for numers tht re not whole. l A = l w w Key ides The re of squre is given y: A = l l = l 2 l A = l 2 Exmple 6 Counting res Count the numer of squres to find the re of the shpe drwn on this entimetre grid. Solution Explntion 6 m 2 There re 5 full squres nd hlf of 2 squres in the tringle, giving 1 more. 1 of 2= 1 2 Exmple 7 Ares of retngles nd squres Find the re of this retngle nd squre. 4 mm 2.5 m 10 mm Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

580 Chpter 11 Mesurement Solution Explntion Are = l w = 10 4 = 40 mm 2 The re of retngle is the produt of the length nd width. Are = l 2 = 2.5 2 = 6.25 m 2 The width is the sme s the length, so A = l l = l 2. (2.5) 2 = 2.5 2.5 Exerise 11D 1 For this retngle drwn on 1 m grid, find eh of the following. the numer of single 1 m squres the length nd the width length width Understnding 2 For this squre drwn on entimetre grid, find the following. the numer of single 1 m squres the length nd the width length width 3 Count the numer of squres to find the re of these shpes. 4 Whih unit of re (mm 2, m 2, m 2, h or km 2 ) would you hoose to mesure these res? Note tht 1 km 2 is muh lrger thn 1 h. re of n A4 piee of pper re of wll of house re of smll frm d re of lrge desert e re of lrge footll ovl f re of nil hed Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 581 Exmple 6 5 Count the numer of squres to find the re of these shpes on entimetre grids. Flueny d e f Exmple 7 6 Find the re of these retngles nd squres. Digrms re not drwn to sle. 10 m 2 m 20 m 11 mm 3.5 m 2 mm Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

582 Chpter 11 Mesurement d 5 m e f Flueny 1.2 mm 2.5 mm g h i 0.8 m 17.6 km 1.7 m 0.9 m 10.2 km 7 Find the side length of squre with eh of these res. Use tril nd error if you re unsure. 4 m 2 25 m 2 144 km 2 8 There re 10 000 m 2 in one hetre (h). Convert these mesurements to hetres. 20 000 m 2 100 000 m 2 5000 m 2 9 A retngulr soer field is to e lid with new grss. The field is 100 m long nd 50 m wide. Find the re of grss to e lid. 10 Glss is to e ut for squre window of side length 50 m. Find the re of glss required for the window. 11 Two hundred squre tiles, eh mesuring 10 m y 10 m, re used to tile n open floor re. Find the re of flooring tht is tiled. 12 A squre hs perimeter of 20 m. Find its re. A squre hs n re of 9 m 2. Find its perimeter. A squre s re nd perimeter re the sme numer. How mny units is the side length? 13 The rpet hosen for room osts $70 per squre metre. The room is retngulr nd is 6 m long y 5 m wide. Wht is the ost of rpeting the room? Prolem-solving 14 Troy wishes to pint grden wll tht is 11 m long nd 3 m high. Two ots of pint re needed. The pint suitle to do the jo n e purhsed only in whole numers of litres nd overs n re of 15 m 2 per litre. How mny litres of pint will Troy need to purhse? 15 A retngulr re of lnd mesures 200 m y 400 m. Find its re in hetres. 16 Find the missing length for eh of these retngles. i ii A = 50 m 2 5 m A = 22.5 mm 2 2.5 mm?? Explin the method tht you used for finding the missing lengths of the retngles ove. Resoning Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 583 17 Explin why the re shded here is extly 2 m 2. 18 A squre hs perimeter P m. If P = 44 m, find the re of the squre. If P is unknown, write n expression for the re of the squre, using P. 4 m 1 m Resoning P = 44 m 19 A squre hs ll its side lengths douled. How does this hnge the re? Investigte nd justify your nswer. Enrihment: Are onversions 20 Use this digrm or similr to help nswer the following. i How mny mm 2 in 1 m 2? ii How mny m 2 in 1 m 2? iii How mny m 2 in 1 km 2? Complete the digrm elow. 10 mm A = 1 m 2 10 mm km 2 m 2 m 2 mm 2 Convert these units to the units shown in rkets. i 2 m 2 (mm 2 ) ii 10 m 2 (m 2 ) iii 3.5 km 2 (m 2 ) iv 300 mm 2 (m 2 ) v 21 600 m 2 (m 2 ) vi 4 200 000 m 2 (km 2 ) vii 0.005 m 2 (mm 2 ) viii 1 km 2 (h) ix 40 000 000 m 2 (h) Guess the re of the pddok in the foreground in squre millimetres. Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

584 Chpter 11 Mesurement 11.5 Are of tringle Put simply, tringle n e onsidered to e hlf retngle, whih is why the formul for the re of tringle looks very muh like the formul for the re of retngle ut with the dded ftor of 1. One of the sides of tringle is lled the 2 se (), nd the height (h) is the distne etween the se nd the opposite vertex. This is illustrted using line tht is perpendiulr (i.e. t 90 ) to the se. Any shpe with ll stright sides (i.e. polygons) n e divided up into omintion of retngles (or squres) nd tringles. This n help to find res of suh shpes. height se Any re of floor with stright sides n e filled with squre nd tringulr tiles. Let s strt: Hlf retngle Look t these tringles. For eh one, disuss why the re ould e onsidered s hlf retngle. Give resons for eh se. 1 2 3 Key ides One side of tringle is lled the se,. The perpendiulr distne from the se to the opposite vertex is lled the height, h. In the third illustrtion elow, the se needs to e extended to help show the height. h h h The re of tringle is given y the formul: A = 1 2 h = 1 se height 2 Note tht 1 2 h is equivlent to h 2. Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 585 Exmple 8 Finding res of tringles Find the re of eh given tringle. 9 m 6 m 10 m 9 m Solution Explntion Are = 1 2 h = 1 2 10 9 = 45 m 2 Use the formul nd sustitute the vlues for se length nd height. Are = 1 2 h = 1 2 6 9 = 27 m 2 The length mesure of 9 m is mrked t 90 to the side mrked 6 m. So 6 m is the length of the se nd 9 m is the perpendiulr height. Exerise 11E 1 For eh of these tringles, wht length would e used s the se? 7 m 8 m 2.1 m Understnding 20 m 2 m d 3 m 5 m 6.3 m 2 For eh of these tringles, wht length would e used s the height? 11 m 6 m 11 mm 15 mm Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

586 Chpter 11 Mesurement 4.1 m 1.9 m d 3.2 mm 4.7 mm Understnding 3 Find the vlue of A in A = 1 h if: 2 = 5 nd h = 4 = 7 nd h = 16 = 2.5 nd h = 10 Exmple 8 4 Find the re of eh tringle given. Flueny 12 m 4 m 5 m 8 m d e 16 m 2.4 m 2 mm 20 m 1 m 3 mm f 7 km g 1.3 m 7 km 2 m h 10 m 4 m i 1.7 m 5 m Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 587 5 Find the re of these tringles, whih hve een drwn on 1 m grids. Give your nswer in m 2. Flueny d 6 A retngulr lok of lnd mesuring 40 m long y 24 m wide is ut in hlf long digonl. Find the re of eh tringulr lok of lnd. 7 A squre pyrmid hs se length of 120 m nd tringulr fe of height 80 m. Find the re of one tringulr fe of the pyrmid. 80 m 120 m Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

588 Chpter 11 Mesurement 8 Eh fe of 4-sided die is tringulr, with se of 2 m nd height of 1.7 m. Find the totl re of ll 4 fes of the die. 9 A frmer uses fening to divide tringulr piee of lnd into two smller tringles, s shown. Wht is the differene in the two res? 18 m 26 m Prolem-solving 40 m 10 A yht must hve two of its sils repled s they hve een dmged y reent storm. One sil hs se length of 2.5 m nd height of 8 m nd the igger sil hs se length of 4 m nd height of 16 m. If the ost of sil mteril is $150 per squre metre, find the totl ost to reple the yht s dmged sils. 11 The re of tringle is 10 m 2 nd its se length is 4 m. Find its height. The re of tringle is 44 mm 2 nd its height is 20 mm. Find its se length. 12 The midpoint, M, of the se of tringle joins the opposite vertex. Is the tringle re split in hlf extly? Give resons for your nswer. M Resoning h Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 589 13 If the vertex C for this tringle moves prllel to the se AB, will the re of the tringle hnge? Justify your nswer. C Resoning A B 14 The re of tringle n e found using the formul A = 1 h. Write down the formul to find 2 the se,, if you re given the re, A, nd height, h. Enrihment: Estimting res with urves 15 This digrm shows shded region tht is 1 2 of 3 m2 = 1.5 m 2. Using tringles like the one shown here, nd y ounting whole squres lso, estimte the res of these shpes elow. d Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

590 Chpter 11 Mesurement 11.6 Are of prllelogrm Rell tht prllelogrm is qudrilterl with two pirs of prllel sides. Opposite sides re of the sme length nd opposite ngles re equl. Like tringle, the re of prllelogrm is found y using the length of one side (lled the se) nd the height (whih is perpendiulr to the se.) Lets strt: Developing the rule Strt this tivity y drwing lrge prllelogrm on loose piee of pper. Ensure the opposite sides re prllel nd then use sissors to ut it out. Lel one side s the se nd lel the height, s shown in the digrm. Cut long the dotted line. Now shift the tringle to the other end of the prllelogrm to mke retngle. Now explin how to find the re of prllelogrm. height se Key ides The re of prllelogrm is given y: A = h where is the se (one of the sides) nd h is the height (perpendiulr to the se). h h Exmple 9 Finding the re of prllelogrm Find the re of these prllelogrms. 5 m 3 m 12 m 2 m Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 591 Solution Explntion A = h = 12 5 = 60 m 2 Choose the given side s the se (12 m) nd note the perpendiulr height is 5 m. A = h = 2 3 = 6 m 2 Use the given side s the se (2 m), noting tht the height is 3 m. Exerise 11F 1 Copy nd omplete the following, using the given vlues of nd h. = 5, h = 7 = 20, h = 3 = 8, h = 2.5 A = h A = A = = = 20 = 20 = 35 = = Understnding 2 For eh of these prllelogrms, stte the side length of the se nd the length of the height tht might e used to find the re. 2 m 4 m 7 m 10 m 6 m 5 m d e 5 m f 1.3 m 1.5 m 1.8 m 6.1 m 2 m 0.9 m 5.8 m Exmple 9 3 Find the re of these prllelogrms. 4 m 7 m 10 m 12 km Flueny 4 m 3 km Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

592 Chpter 11 Mesurement d 7 m 2.5 m e 3 m f 2 m Flueny 15 m 2.1 m g h 7 m i 2.1 m 1 m 1.8 m 2 m 3 m 16 mm 20 mm 4 These prllelogrms re on 1 m grids (not to sle). Find their re. 11 mm d 5 The floor of n offie spe is in the shpe of prllelogrm. The longest sides re 9 m nd the distne etween them is 6 m. Find the re of the offie floor. 6 Find the height of prllelogrm when its: re = 10 m 2 nd se = 5 m re = 28 m 2 nd se = 4 m re = 2.5 mm 2 nd se = 5 mm Prolem-solving 7 Find the se of prllelogrm when its: re = 40 m 2 nd height = 4 m re = 150 m 2 nd height = 30 m re = 2.4 km 2 nd height = 1.2 km 8 A lrge wll in the shpe of prllelogrm is to e pinted with speil red pint, whih osts $20 per litre. Eh litre of pint overs 5 m 2. The wll hs se length of 30 m nd height of 10 m. Find the ost of pinting the wll. Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 593 9 A proposed retngulr flg for new ountry is yellow with red stripe in the shpe of prllelogrm, s shown. Find: Find the re of the red stripe. Find the yellow re. 30 m 70 m 60 m Prolem-solving 10 Explin why this prllelogrm s re will e less thn the given retngle s re. Resoning 5 m 5 m 10 m 10 m 11 A prllelogrm inludes green tringulr re, s shown. Wht frtion of the totl re is the green re? Give resons for your nswer. 12 The re of prllelogrm n e thought of s twie the re of tringle. Use this ide to omplete this proof of the rule for the re of prllelogrm. Are = twie tringle re = 2 = h Enrihment: Glss fçde 13 The Puert de Europ (Gte of Europe) towers re twin offie uildings in Mdrid, Spin. They look like norml retngulr glss-overed skysrpers ut they len towrds eh other t n ngle of 15 to the vertil. Two sides re prllelogrms nd two sides re retngles. Eh tower hs vertil height of 120 m, slnt height of 130 m nd squre se of side 50 m. All four sides re overed with glss. If the glss osts $180 per squre metre, find the ost of overing one of the towers with glss. (Assume the glss overs the entire surfe, ignoring the ems.) Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

594 Chpter 11 Mesurement 11.7 Are of omposite shpes The res of more omplited shpes n e found y dividing them up into more simple shpes, suh s the retngle nd tringle. We n see this in n eril view of ny Austrlin ity. Suh view will show tht mny ity streets re not prllel or t right ngles to eh other. As result this uses ity loks to form interesting shpes, mny of whih re omposite shpes mde up of retngles nd tringles. Streets, prks nd uildings form omplex shpes tht n e mde up of tringles nd retngles. Let s strt: Dividing lnd to find its re Working out the re of this piee of lnd ould e done y dividing it into three retngles, s shown. Cn you work out the re using this method? Wht is nother wy of dividing the lnd to find its re? Cn you use tringles? Wht is the esiest method to find the re? Is there wy tht uses sutrtion insted of ddition? 30 m 20 m 30 m 10 m 20 m Key ides Composite shpes re mde up of more thn one simple shpe. The re of omposite shpes n e found y dding or sutrting the res of simple shpes. A squre plus tringle A retngle sutrt tringle Exmple 10 Finding the re of omposite shpes Find the re of eh of these omposite shpes. 12 m 5 m 9 m 4 m 6 m Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 595 Solution Explntion A = l w + 1 2 h = 9 5 + 1 2 3 5 = 45 + 7.5 = 52.5 m 2 Divide the shpe into retngle nd tringle nd find the missing lengths. 9 m 3 m 5 m 5 m 9 m 12 9 = 3m A = l 2 1 2 h = 6 2 1 2 6 4 = 36 12 = 24 m 2 Sutrt the tringle ( 1 6 4) t the top of the shpe 2 from the lrger squre (6 6). 6 m 4 m 6 m 6 m Exerise 11G 1 Copy these digrms nd drw dotted line where you might divide these shpes into two more simple shpes. Understnding 2 To find the re of eh of the following shpes, deide if the esiest method would involve the ddition of two shpes or the sutrtion of one shpe from nother. Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

596 Chpter 11 Mesurement 3 Copy nd omplete the solutions for the res of these shpes. 1 m 5 m 4 m 2 m 1 m 4 m 3 m 13 m A = l 2 + A = lw = 1 2 + 3 = 8 1 2 = + = = m 2 = m 2 Understnding Exmple 10 4 Find the re of these omposite shpes y dding together the re of simpler shpes. 3 m 10 mm Flueny 4 m 10 mm 6 m 40 mm 2 m d 5 m 3 m 8 m 9 m 3 m e 21 m 17 m 9 m f 3 km 10 km 6 km Exmple 10 5 Use sutrtion to find the re of these omposite shpes. 3 m 2 m 6 m 3 m 7 m 3 m 10 m Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 597 e 2 m 6 m 5 m d f 4 m 8 m 9 m 1 m 9 m 2.5 m Flueny 14 m 20 m 4 m 6 Find the res of these omposite shpes. 8 m 4 m 5 m 2 m Prolem-solving 4 m 15 m 20 m 7 By finding the missing lengths first, lulte the re of these omposite shpes. 2 m 3.5 m 12 m 4 m d 2 m 5 m 3.5 m 2 m 1 m 6 m Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

598 Chpter 11 Mesurement 8 A wll hs three squre holes ut into it to llow for windows, s shown. Find the remining re of the wll. 2.4 m 6 m 1.2 m Prolem-solving 9 A ftory floor, with dimensions shown opposite, is to e overed with linoleum. Inluding underly nd instlltion, the linoleum will ost $25 per squre metre. The udget for the jo is $3000. Is there enough money in the udget to over the ost? 12 m 10 m 4 m 5 m 10 Explin why using sutrtion is sometimes quiker thn using ddition to find the re of omposite shpe. Refer to the digrm s n exmple. Resoning 11 The 4-sided shpe lled the trpezium hs one pir of prllel sides. For the trpezium shown opposite, is it possile to find the se length of eh tringle on the sides? Justify your nswer. Cn you ome up with method for finding the re of trpezium using the retngle nd tringles shown in the digrm? Use digrms to explin your method. 6 m 10 m 5 m Enrihment: Adding to infinity 12 The squre given opposite, whih hs n re of 1 unit, is divided to show the res of 1 2, 1 4, 1 8,... Similr to the one shown opposite, drw your own squre, showing s mny frtions s you n. Try to follow the spirl pttern shown. Note: The igger the squre you strt with, the more squres you will e le to show. i Write the next 10 numers in this numer pttern. 1,... 2, 1 4, 1 8 ii Will the pttern ever stop? Wht is the totl re of the strting squre? d Wht do your nswers to prts ii nd tell you out the nswer to the sum elow? 1 2 + 1 4 + 1 8 + 1 +... (ontinues forever) 16 1 8 1 4 1 32 1 16 1 1 2 1 Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 599 11.8 Volume of retngulr prisms The mount of spe inside 3-dimensionl (3D) ojet is lled volume. Volume is mesured in ui units suh s the ui entimetre, whih is 1 m long, 1 m wide nd 1 m high. Just like the topis of length nd re, different units n e seleted, depending on the size of the volume eing mesured. For exmple, the volume of wter in the se ould e mesured in ui kilometres nd the volume of onrete poured from ement mixing truk ould e mesured in ui metres. Let s strt: Volume We ll know tht there re 100 m in 1 m, ut do you know how mny ui The Pifi Oen ontins hundreds of thousnds of ui kilometres of wter. entimetres re in 1 ui metre? Try to visulise 1 ui metre 1 metre long, 1 metre wide nd 1 metre high. Guess how mny ui entimetres would fit into this spe. Desrie method for working out the ext nswer. Explin how your method works. Volume is mesured in ui units. The ommon metri units for volume inlude: ui millimetres (mm 3 ) 1 mm 1 mm 1 mm (Not drwn to sle.) Key ides ui entimetre (m 3 ) 1 m 1 m 1 m ui metre (m 3 ) (Not drwn to sle.) 1 m 1 m 1 m Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

600 Chpter 11 Mesurement Key ides ui kilometre (km 3 ) (Not drwn to sle.) 1 km 1 km 1 km The volume of retngulr prism is given y the formul: V = length width height = lwh A retngulr prism is lso lled uoid. l h w V = lwh The volume of ue is given y: V = l l l = l 3 l l l V = l 3 Exmple 11 Finding the volume of uoid Find the volume of this retngulr prism. Solution 8 m Explntion 4 m 3 m V = lwh = 8 3 4 = 96 m 3 Use the formul for the volume of retngulr prism, then sustitute the three lengths into the formul. Exerise 11H 1 For eh of these solids, ount the numer of ui units to find its volume. Understnding Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 601 d Understnding e f 2 Copy nd omplete the working shown for eh of these solids. 4 m 2 m 3 m 6 m 2 km 2 km 1 m 3 m 2 km V = lwh V = lwh V = l 3 = 4 = 1 = 2 = m 3 = = km 3 Exmple 11 3 Find the volume of these retngulr prisms. 3 m 4 m 7 m 5 m 2 m 1 m Flueny Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

602 Chpter 11 Mesurement 7 m d Flueny 7 m 2 m 3 m e f 10 km 1.4 mm g 1 m h 1.5 km 10 m 5 km 4 A fruit ox is 40 m long, 30 m wide nd 20 m high. Find its volume. 5 A shipping ontiner is 3 m wide, 4 m high nd 8 m long. Find its volume. 6 A short retngulr ruler is 150 mm long, 40 mm wide nd 2 mm thik. Find its volume. 7 There is enough ie on Erth to fill ue of side length 300 km. Find the pproximte volume of ie on Erth. Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 603 8 These solids re mde up of more thn one retngulr prism. Use ddition or sutrtion to find the volume of the omposite solid. 4 m 3 m Prolem-solving 4 m 3 m 5 m 8 m 2 m 2 m 10 m 4 m 9 m 2 m 9 A ox mesuring 30 m long, 20 m high nd 30 m wide is pked with mthoxes, eh mesuring 5 m long, 2 m high nd 3 m wide. How mny mthoxes will fit in the ox? 10 The outside dimensions of losed wooden ox re 20 m y 20 m y 20 m. If the ox is mde from wood tht is 2 m thik, find the volume of ir inside the ox. 11 The re of one fe of ue is 25 m 2. Find the ue s volume. The perimeter of one fe of ue is 36 m. Find the ue s volume. 12 We n find the re of this shded tringle y thinking of it s hlf retngle. Use the sme ide to find the volume of eh of these solids. Resoning Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

604 Chpter 11 Mesurement 13 Find the height of these retngulr prisms with the given volumes. Use tril nd error if you prefer. i ii? Resoning 4 m V = 16 m 3 2 m? 3 m V = 45 m 3 iii iv 4 m? 2 m V = 56 m 3 9 m V = 54 m 3 2 m Cn you explin method tht lwys works for finding the height of retngulr prism? Use V, l nd w to write rule for h. Enrihment: Cui onversions 14 The digrm shows 1 m 3 lok tht is divided into ui millimetres. i How mny mm 3 re there long one edge of the ue? ii How mny mm 3 re there in one lyer of the ue? (Hint: How mny ues sit on the se?) iii How mny lyers of mm 3 re there in the ue? iv Use your nswers from prts i to iii ove to now lulte how mny mm 3 there re in 1 m 3. Use similr method to lulte the numer of: i m 3 in 1 m 3 ii m 3 in 1 km 3 Complete the digrm shown. km 3 m 3 m 3 mm 3 1 m 1 m 1 m Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 605 11.9 Cpity Cpity reltes to the volume of fluid or gs tht ontiner n hold. For exmple, the pity of wter tnk my e 5000 litres, or frmer s wter llotion might e 300 meglitres (mening 300 million litres). The si unit is the litre, whih ontins 1000 m 3 of spe. Other ommon metri units for pity inlude the millilitre, kilolitre nd meglitre. There is ler link etween pity nd volume, s they oth relte to the spe oupied y 3-dimensionl ojet. Let s strt: Wter ontiners Wil, Tony nd Ethn eh ring ontiner to ollet some wter from fountin. Wil sys his ontiner holds 2 litres. Tony sys his ontiner holds 2000 m 3. Ethn sys his ontiner holds 2000 millilitres. Who n ollet the most wter? Give resons for your nswer. Irrigtion hnnels rry meglitres of wter to frms. Cpity is the volume of fluid or gs tht n ojet n hold. Common metri units inlude: 1 litre (L) = 1000 millilitres (ml) 1 kilolitre (kl) = 1000 litres (L) 1 meglitre (ML) = 1000 kilolitres (kl) 1000 1000 1000 ML kl L ml 1000 1000 1000 Key ides Relting volume nd pity 3 1 m = 1 ml 3 1 m = 1000 L = 1 kl M I L K M I L K 1 L (1000 ml) 1000 m 3 Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

606 Chpter 11 Mesurement Exmple 12 Converting units for pity Convert to the units shown in rkets. 500 ml (L) 3 ML (L) Solution 500 ml = 500 1000 = 0.5 L 3 ML = 3 1000 kl = 3 1000 1000 L = 3 000 000 L Explntion When onverting to lrger unit, divide. There re 1000 ml in 1 L. There re 1000 kl in 1 ML nd 1000 L in 1 kl. So 1 ML is 1 million litres. Exmple 13 Converting m 3 to litres Find the pity of this ontiner, in litres. Solution Explntion 10 m 20 m V = 20 10 10 = 2000 m 3 = 2000 ml = 2000 1000 L = 2 L V = lwh 1 m 3 = 1 ml There re 1000 ml in 1 litre. Exerise 11I 1 Complete these sentenes. 1 ml ontins the volume of m 3. 1 L ontins ml. 1 L ontins m 3. d 1 kl ontins L. e 1 ML ontins kl. Understnding 2 Cirle or write down whih volumes re the sme. 1 L, 10 kl, 1000 ml, 1 m 3, 1000 m 3 1 m 3, 100 L, 1000 L, 1000 ML, 1 kl Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 607 3 From options A to F, hoose the pity tht est mthes the given ontiner. tespoon A 18 L up B 250 ml ottle C 10 kl d kithen sink D 20 ml e wter tnk E 45 ML f wter in lke F 0.8 L Understnding Exmple 12 4 Convert to the units shown in rkets. 2 L (ml) 0.1 L (ml) 6 ML (kl) d 24 kl (L) e 2000 L (kl) f 3500 ml (L) g 70 000 ml (L) h 2500 kl (ML) i 0.257 L (ml) j 9320 ml (L) k 3.847 ML (kl) l 47 000 L (kl) m 0.5 kl (L) n 91 000 kl (ML) o 0.42 L (ml) p 170 L (kl) 5 Red these sles to determine the mount of wter in eh of the ontiners. 25 4 1 L 20 3 750 15 2 500 10 1 250 5 m 3 ml ml Flueny Exmple 12 6 A up of 200 ml of wter is dded to jug lredy ontining 1 L of wter. Find the totl volume in: ml L 7 Convert to the units shown in rkets. 6 ML (L) 320 000 L (ML) 0.004 kl (ml) d 992 700 ml (kl) 8 A frmer purhses 3.3 ML of wter for her pple orhrd. How mny litres is this? Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

608 Chpter 11 Mesurement Exmple 13 9 Find the pity of eh of these ontiners, in litres. e 10 m 6 m 10 m 10 m 50 m 9 m 15 m 3 m d f 8 m 32 m 32 m 5 m 13 m 12 m 21 m 10 A swimming pool in the shpe of retngulr prism hs length 50 m, width 25 m nd depth 2 m. Find the swimming pool s: volume, in m 3 pity, in L 11 A dripping tp leks out 10 ml every minute. If there re 50 drips per minute, find the volume of one drip. Find the pproximte volume of wter, in litres, tht hs leked from tp fter the following time periods. i 100 minutes ii 1 hour iii 1 dy iv 1 yer Prolem-solving Flueny 12 A dose of 12 ml of mediine is to e tken twie eh dy from 0.36 L ottle. How mny dys will it tke to finish the mediine? 13 A gs ottle ontins 50 L of liquid gs. If the liquid gs is used t rte of 20 ml per minute, how mny hours will the gs ottle lst? Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 609 14 A ity s dms hve 2 million meglitres of wter nd the verge dily onsumption of the ity s people is 400 L per dy per person. If the ity s popultion is 5 million people, how long will the dm supply lst without further wter thment? 15 If x is ny numer, then x litres is the sme s 1000 x = 1000 x millilitres euse there re 1000 ml in 1 L. Write expressions for x L in the following units. m 3 m 3 kl d ML Resoning Prolem-solving 16 A retngulr prism hs length l m, width w m nd height h m. Write n expression for the pity of the ontiner mesured in: i m 3 ii ml iii L iv kl A retngulr prism hs length l m, width w m nd height h m. Write n expression for the pity of the ontiner mesured in: i m 3 ii L iii kl iv ML Enrihment: Added depth 17 A ontiner is 10 m long, 5 m wide nd 8 m high. Find the depth of wter when the following mounts 8 m of wter re poured in. (Rememer: 1 ml = 1 m 3.) 5 m i 400 ml ii 200 ml iii 160 ml 10 m After dding 200 ml, further 30 ml is dded. Wht is the inrese in depth? A 1-litre ontiner of milk hs se re of 8 m y 7 m. After 250 ml of milk is poured out, wht is the depth of the milk remining in the ontiner? Give your nswer to the nerest mm. Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

610 Chpter 11 Mesurement 11.10 Mss nd temperture The sles for oth mss nd temperture re sed on the properties of wter. In Frne in 1795, the grm ws defined s eing the weight of 1 m 3 of wter t 0 C. Lter it ws redefined to e the weight t 4 C, s this is onsidered to e the temperture t whih wter is the most dense. So, 1 litre of wter is very lose to 1 kilogrm, whih is the si unit for mss. Other units for mss inlude the tonne, grm nd milligrm. A smll r hs mss of out 1 tonne nd 20-ent oin hs mss of out 11 grms. Temperture tells us how hot or old something is. Anders Celsius (1701 1744), Swedish sientist, worked to define sle for temperture. After his deth, temperture ws offiilly defined y: 0 C (0 degrees Celsius) the freezing point of wter. 100 C (100 degrees Celsius) the oiling point of wter (t one stndrd degree of pressure). This is still the ommon understnding of degrees Celsius. As mentioned in Chpter 10, Fhrenheit is nother sle used for temperture. This is investigted further in the Enrihment questions. A smll r hs mss of out 1 tonne. Let s strt: Choose unit of mss Nme five ojets of whih their mss would ommonly e mesured in: tonnes kilogrms grms milligrms Is it possile for the temperture to drop elow 0 C? How is this mesured nd n you give exmples of ples or situtions where this might e the se? Ie melts t 0 C. Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 611 The si unit for mss is the kilogrm (kg). 1 litre of wter hs mss tht is very lose to 1 kilogrm. Metri units for mss inlude: 1000 1000 1000 1 grm (g) = 1000 milligrms (mg) t kg g mg 1 kilogrm (kg) = 1000 grms (g) 1 tonne (t) = 1000 kilogrms (kg) 1000 1000 1000 Key ides The ommon unit for temperture is degrees Celsius ( C). 0 C is the freezing point of wter. 100 C is the oiling point of wter. Exmple 14 Converting units of mss Convert to the units shown in rkets. 2.47 kg (g) 170 000 kg (t) Solution Explntion 2.47 kg = 2.47 1000 g = 2470 g 1 kg = 1000 g Multiply euse you re hnging to smller unit. 170 000 kg = 170 000 1000 t = 170 t 1 t = 1000 kg Divide euse you re hnging to lrger unit. Exerise 11J 1 Cirle or write down whih mss mesurements re the sme. 1 kg, 100 g, 1000 g, 10 t 1000 mg, 10 kg, 1 g, 1000 t 2 From options A to F, hoose the mss tht est mthes the given ojet. humn hir A 300 g 10-ent oin B 40 kg ottle C 100 mg d lrge ook D 1.5 kg e lrge g of snd E 13 t f truk F 5 g Understnding 3 From options A to D, hoose the temperture tht est mthes the desription. temperture of offee A 15 C temperture of tp wter B 50 C temperture of oven C -20 C d temperture in Antrti D 250 C Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

612 Chpter 11 Mesurement Exmple 14 4 Convert to the units shown in rkets. 2 t (kg) 70 kg (g) 2.4 g (mg) d 2300 mg (g) e 4620 mg (g) f 21 600 kg (t) g 0.47 t (kg) h 312 g (kg) i 27 mg (g) j 3 4 t (kg) k 1 kg (g) l 10.5 g (kg) 8 m 210 000 kg (t) n 0.47 t (kg) o 592 000 mg (g) p 0.08 kg (g) Flueny 5 Red these mss sles. kg 1 2 34567 6 2 10 1416 20 g 6 Red these temperture sles. C 15 10 5 C 40 38 36 C 20 15 34 10 d 50 100 0 150 200 250 C 300 e 1 2 C f 18 9 27 36 C 45 7 A smll truk delivers 0.06 t of stone for grden. Write the mss of stones using these units. kg g mg 8 A ox ontins 20 loks of heese, eh weighing 150 g. Wht is the pproximte mss of the ox in the following units? g kg Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 613 9 The temperture of wter in up is initilly 95 C. After hlf n hour the temperture is 62 C. Wht is the drop in temperture? Flueny 10 An oven is initilly t room temperture of 25 C. The oven dil is turned to 172 C. Wht is the expeted inrese in temperture? 11 Add ll the mss mesurements nd give the result in kg. 3 kg, 4000 g, 0.001 t 2.7 kg, 430 g, 930 000 mg, 0.0041 t 12 Arrnge these mss mesurements from smllest to lrgest. 2.5 kg, 370 g, 0.1 t, 400 mg 0.000 32 t, 0.41 kg, 710 g, 290 000 mg 13 The highest nd lowest tempertures reorded over 7-dy period re s follows. Prolem-solving Dy 1 2 3 4 5 6 7 Lowest temperture ( C) 8 6 10 9 7 8 10 Highest temperture ( C) 24 27 31 32 21 19 29 Whih dy hd the lrgest temperture inrese? Wht is the lrgest temperture drop from the highest temperture on one dy to the lowest temperture on the next dy? Wht would hve een the finl temperture on Dy 7 if the temperture inrese hd een 16 C? 14 A 10 kg g of flour is used t rte of 200 g per dy. How mny dys will the g of flour lst? 15 A ot hs weight limit of 3.5 t rrying pity. Loded onto the ot re 1500 tins of offee t 500 g eh, 36 gs of grin t 20 kg eh, 190 oxes of too t 5.5 kg eh nd 15 people, verging 80 kg eh. Is the lod too muh for the weight limit of the ot? Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

614 Chpter 11 Mesurement 16 A truk tre mss (i.e. mss with no lod) is 13.2 t. The truk s gross mss is 58.5 t. This is the totl mximum mss llowed, inluding the lod. Wht is the mximum lod the truk n rry? The truk is loded with 120 timer ems t 400 kg eh. Will it exeed its gross weight limit? 17 Wter weighs 1 kg per litre. Wht is the mss of these volumes of wter? 1 ml 1 kl 1 ML Resoning Prolem-solving 18 The ontiners shown elow re filled with wter. Clulte the mss of wter in eh ontiner, in kg. 15 m 2 m 15 m 40 m 12 m 20 m 1 m 19 The kelvin (K) is temperture unit used y mny sientists, where 2730 K is pproximtely 0 C. (The kelvin used to e lled the degree kelvin or K.) An inrese in 1 K is the sme s n inrese in 1 C. Write the following tempertures in C. i 283 K ii 300 K iii 1000 K Write the following tempertures in kelvins. i 0 C ii 40 C iii -273 C Liquid nitrogen freezes t -210 C nd oils t -196 C. Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 615 Enrihment: Fhrenheit 20 Dniel Fhrenheit (1686 1736) proposed the Fhrenheit temperture sle in 1724. It ws ommonly used in Austrli up until the mid 20th entury, nd is still used tody in the United Sttes. 32 F is the freezing point of wter. 212 F is the oiling point of wter. Wht is the differene etween the temperture, in Fhrenheit, for the oiling point of wter nd the freezing point of wter? 1 F is wht frtion of 1 C? 1 C is wht frtion of 1 F? d To onvert from F to C, we use the formul C = (F 32) 5. Convert these Fhrenheit 9 tempertures to C. i 32 F ii 68 F iii 140 F iv 221 F e Find the rule to onvert from C to F. Test your rule to see if it works nd write it down. Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

616 Chpter 11 Mesurement Investigtion Opl mining Greg, Slly nd Alston pply for mining liene to look for opls t Cooper Pedy in South Austrli. They re required to hoose n re nd mrk it out with speil ornge tpe so tht others will know whih res re lredy tken. Their length of tpe is 200 m. Squre mining res They first deide to mrk out n re s squre. Mke drwing of their squre re. Clulte the side length nd re nd show this on your digrm. Also show ny working. Retngulr mining res They then hnge the mining re nd experiment with different side lengths. Show 3 possile lengths nd res for retngulr mining sites. Complete tle similr to this one. Fill in the missing numers for the side lengths given, then dd your own retngle mesurements from prt ove. Length Width Perimeter Are 10 20 35 200 200 200 200 200 200 Are there ny retngles tht give lrger re thn the squre mining re from ove? Cirulr mining res They now deide to try to rrnge the tpe to form irle. For this setion you will need the rule to lulte the distne round irle (irumferene). The irumferene C is given y C = 2 π r where r is the length of the rdius nd π 3.14. r C Clulte the rdius of the irle orret to one deiml ple. Use tril nd error (guess nd hek) tehnique nd rememer tht the irumferene will e 200. Explin nd show your method using tle of vlues. Clulte the re of the irulr mining re orret to the nerest squre metre. Use the speil rule for the re of irle A whih is given y A = π r 2. The lrgest re Compre the res mrked out with the 200 m tpe y Greg, Slly nd Alston. Comment on ny differenes. Whih shpe gives the lrgest re for the given perimeter? Would your nswer e the sme if ny shpe were llowed to e used? Explin. Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 617 1 Without mesuring, stte whih line looks longer: A or B? Then mesure to hek your nswer. A OR 2 You hve two stiks of length 3 m nd 5 m, oth with no sles. How might you mrk length of 1 m? 3 Count squres to estimte the re of these irles. 4 A house roof hs 500 m 2 of re. If there is 1 mm of rinfll, how muh wter, in litres, n e olleted from the roof? B Puzzles nd hllenges 5 Work out the volume of this retngulr prism with the given fe res. 12 m 2 6 m 2 8 m 2 6 Find the re of the shded region. 7 m 3 m 7 A ue of side length 20 m ontins 5 L of wter. Wht is the depth of wter in the ue? Wht is the inrese in depth if 1.5 L is dded to the ue of wter? 8 These two retngles overlp, s shown. Find the totl re of the shded region. 5 m 8 m 3 m 2 m 4 m 6 m Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

618 Chpter 11 Mesurement Chpter summry 2 m Prllelogrm 5 m Romn 16 digits = 12 inhes = 1 foot 5 feet = 1 pe 1000 pes = 1 mile Imperil 12 inhes = 1 foot 3 feet = 1 yrd 1760 yrds = 1 mile A = 6h = 5 2 = 10 m 2 Metri mm 2 m 2 m 2 h km 2 1 h = 10000 m 2 A = lw = 4 2 = 8 m 2 Retngle 4 m Are 2 m Mesurement 9 m Squre Tringle 3 m 1 A = h 2 1 = 3 2 2 = 3 m 2 A = l 2 = 9 2 = 81 m 2 2 m Composite shpes 18 m 10 m 8 m 19 m 1 A = l w + h 2 1 = 18 10 + 10 9 2 = 225 m 2 Metri Volume 10 mm = 1 m 100 m = 1 m 1000 m = 1 km Length Cpity 1 L = 1000 ml 1 kl = 1000 L 1 ML = 1000 kl nd 1 ml = 1 m 3 1 m 3 = 1000 L 2.1 m 1.5 m Perimeter 3 m P = 2 2.1 + 1.5 + 3 = 8.7 m Temperture C (Celsius) Mss 1 g = 1000 mg 1 kg = 1000 g 1 t = 1000 kg Retngulr prism 2 m 5 m 4 m V = lwh = 5 4 2 = 40 m 3 mm 3 m 3 m 3 km 3 Metri Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 619 Multiple-hoie questions 1 Whih of the following re imperil units? A m B pe C digit D yrd E litre 2 Shonli uys 300 m of wire tht osts $2 per metre. How muh does she py for the wire? A $150 B $600 C $1.50 D $3 E $6 3 The tringle given hs perimeter of 20 m. Wht is the missing se length? A 6 m B 8 m C 4 m D 16 m E 12 m 8 m 4 The re of retngle with length 2 m nd width 5 m is: A 10 m 2 B 5 m 2 C 5 m D 5 m 3 E 10 m 5 A tringle hs se length 3.2 m nd height 4 m. Wht is its re? A 25.6 m 2 B 12.8 m C 12.8 m 2 D 6 m E 6.4 m 2? 6 The totl re of this omposite shpe is: A 56 km 2 B 45.5 km 2 C 35 km 2 D 10.5 km 2 E 24.5 km 2 3 km 5 km 7 km 7 A ue hs side length of 3 m. Its volume is: A 27 m 3 B 9 m 2 C 3 m D 9 m 3 E 36 m 3 8 2000 m 3 is the sme s: A 2 m 3 B 2 L C 2 kl D 2 ml E 2 t 9 9 tonnes of iron ore is eing loded onto ship t rte of 20 kg per seond. How mny minutes will it tke to lod ll of the 9 tonnes of ore? A 0.75 min B 45 min C 7.3 min D 450 min E 7.5 min 10 The se length of prllelogrm is 10 m nd its re is 30 m 2. The prllelogrm s height is: A 10 m B 3 m C 30 m D 3 m 2 E 10 m 2 Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

620 Chpter 11 Mesurement Short-nswer questions 1 Using the Romn system, stte how mny: i digits in 1 foot ii pes in 1 mile Using the imperil system, stte how mny: i feet in 1 yrd ii inhes in 1 foot Using the metri system, stte how mny: i millimetres in 1 m ii entimetres in 1 km 2 Convert to the units shown in rkets. 5 m (mm) 200 m (m) 3.7 km (m) d 421 000 m (km) e 7.1 kg (g) f 24 900 mg (g) g 28 490 kg (t) h 0.009 t (g) i 4000 ml (L) j 29 903 L (kl) k 0.4 ML (kl) l 0.001 kl (ml) m 1 dy (min) n 3600 s (min) o 84 h (dys) p 2.5 h (s) 3 Red these sles. m 1 2 3 m 1 2 3 1 2 3 kg 4 5 d 10 8 6 4 2 L 4 Find the perimeter of these shpes. 4 m 7.1 m 3.2 m 5 m d 9 m 8 km 9 km 7 km 4 km Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 621 e f 6 m 0.4 mm 5 Find the re of eh of the following shpes. 2 km 4.9 m 7 km 9 m d 6 m 15 m 4 m e 8 m f 1 m 3.5 m 1 m 1 m 3 m g 7 m h 4 m 4 m 2 mm 5 mm i 9 m j 2 m 9 m 22 m 15 m 6 m 4 m 12 m k 2 m l 1.5 km 7 m 0.6 km Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

622 Chpter 11 Mesurement 6 Find the volume ontined in eh of these solids. 1 m ues 3 m 1 m 2.5 m 4 mm 7 A retngulr fish tnk is of length 60 m, width 40 m nd height 30 m. Give the tnk s pity in: m 3 ml L 8 Arrnge these mesurements from smllest to lrgest. 3 t, 4700 kg, 290 000 g, 45 mg 50 000 ml, 1 ML, 51 L, 0.5 kl Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.

Mesurement nd Geometry 623 Extended-response questions 1 A truk rries lrge retngulr ontiner of dimensions 6 m long, 3 m wide nd 2 m high. The truk weighs 15.4 tonnes without its lod. Find the re of the se of the ontiner in: i m 2 ii m 2 Find the volume of the ontiner in m 3. How mny litres of wter ould the truk hold in the ontiner? d Sine 1 L of wter weighs 1 kg, give the weight of the truk if the ontiner ws filled with wter. Give your nswer in tonnes. e The truk ompletes three journeys, whih tke, on verge, 1 hour, 17 minutes nd 38 seonds per trip. Wht is the totl time for the three journeys? 2 Lhln uilds re trk round the 36.3 m outside of his fmily house lok. The lok omines retngulr nd tringulr re, s shown in the digrm. 15 m house How fr is one omplete iruit of the trk? 10 m Lhln n jog 10 lps t out 18 m 33 seonds eh. Wht is the totl time, in minutes nd seonds, tht it tkes him to omplete the 10 lps? Wht is the totl re of the lok? d The house oupies 100 m 2 nd the rest of the lok is to hve instnt turf, osting $12 per squre metre. Wht will e the ost for the instnt turf? e The house sits on onrete sl tht is 50 m deep. Wht is the volume of onrete, in m 3? Dvid Greenwood, Frn Frnk, Jenny Goodmn, Bryn Humerstone, Justin Roinson, Jennifer Vughn 2010 Cmridge University Press Photoopying is restrited under lw nd this mteril must not e trnsferred to nother prty.