b 4. This quarter is approximately 2.5 em wide. Estimate how long the line is using the quarter as a referent.

Transcription

1 Name: Class: -:;:::======~_Date: _ ""--<'::'bapter1 and 2 Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. What is Canada's official measurement system? a. avoirdupois system g Sl system b. imperial system d. US system 2. A non-standard measuring unit that you choose to use is called a(n) a. - caliper c. metre b. referent 3. What reading is shown on the caliper image below? a mm b mm c mm d mm ~ b 4. This quarter is approximately 2.5 em wide. Estimate how long the line is using the quarter as a referent. I /I ( 1..5 ern ~5.0em ~7.5cm c. ]0.0 ern d em

2 Name: Identify the most appropriate imperial measurement unit to use when estimating the perimeter of this figure. ~ a. c. mile d. yard 6. Identify which of the following measuring instruments is best for measuring the length of a soccer field. a. caliper c. ruler b. metre stick trundle wheel 7. What measurement is shown on the imperial caliper? 00'\-ta in. b in. c in. d in. 8. Determine the measurement shown on the imperial caliper. Om\\- a in. b in. c in. d in. 9. A florist requires 12 in. of ribbon for each bouquet of flowers he creates. How many bouquets will he be able to create from 10 yd of ribbon? \ 0 ~ v: 36;. ('\ =. 3~0 \('\ a. 120 c. 22 \ >(G\. b ~3toc).2; \ d- \ 10. Your dining room measures 8 m by 8 m. You have found the perfect carpet for the room, but it is sold in square yards. To the nearest hundredth, how many square yards do you need? a yd 2 c. 17.S0yd 2 U.).e. \'to. -=- O.q\L\L\ r1\ b yd? -6 ~ v: \ ~ d. ~ <:0:1 ~ \.yc\ O q\l\l\ rf\2

3 ~ J11. ' 9- yr< 'f- \. T z: ~ f',t- / " O\~Dl.\ 6 fj) - r -<>. \ Name: -+-_. (La V\l"\)\~ T'--e\- J. ( ~v5tod-~ ~ \U? ~ lo..l.\(\ :==- 1- \ r-, How long IS 2 III III feet and inches? Express your an'swe'rto the nearest inch. a. 0' 79" c. 6' 0" b. 7' 9" 6' 7" (.; 12. Convert :J3l the [~tt i-;0] in. to centimetres. Round your answer to the nearest tenth. L\- re- \ (\. = 4..3\;).. fi 5 \{\ a. 11.0cm. b. 3.9cm d. 14.1cm l.\.3\?-s 0< X 'a,~i.-\(rn \o~q5 (-t 13. A low bridge has a posted height of7 ft 6 in. If your truck is 2.3 m high, how many centi~itfe's over or u C-,(( _. Dri) 1.4 em over c.'r\a.v'\.~ c ern over....tt _. A-,.?6b ~ lb. 1.4 cm under ~ d em under 6 ~)E ~ 54 ~ j.. \M :: O,b2.~ ~'by~ 6.9lL :(p.\~?>6 \-o.\s?l\)m~-a. d-'b~r<l.' ~ \o()~ (Y' A 14. The carpet Caleigh has chosen for her new recreation room costs $8.50 per square metfe. The room measures 20 ft by 18 ft. To the nearest dollar, how much will it cost Caleigh to carpet this $284' c. $3060 A = t:,. (J'\ la rv\ 'J "0 bl\ M b. $933 d. $ ~ = '3~. '-\-4 S ('(1 ').. c:\i r-, Co:>\- '=.$ <a. '50.y. '3 ":>,, 4~ 5 ~~~'J \ -L1-15. A circular swimming pool has a diameter of 8.6 m. It is filled with water to a height of 1.6 m. HO\~ much bridge height will it be? ~ 1- ~ t ~ O. '?'>O'-\ CO C0 ~ 'd. ~, '3 ''3 b () w~ter is in the pool, to the nearest hundred litres? Hint: 1000 L = 1 m", f) L <.'~;C";i,;.~. a L b L '> d= :0, ~ (Y\ '.10\ c).\ c..~\; (lc\tv' ~ Lo.. {eo. 0t \:>0 s.e )(." "b,.,. -: - ~ ("-=- ~ 2> fy'\ "=- \ \ 'f ::L '" n,,=\..bm ~ \:( 1- i.\-. 3:l- ~ \ ~to '\I ~ q~.~ ry\~ \1",,\ ',(\ "Lit -:. a~. q ~ "A CD 92900L \j =\C\'J, qoo L\ \C)CO.!:- c L 'lu ~\ \~ b 16. Determine the volume of the right pyramid. L '-l 0\ -==-i tl-l(a('e<!t O~ be\.{ ') -,(." 1.0 I'd " <~ -L C-t )C.w) ~ ~ 3 V~ _, (\.Q 'i- \\1. Yo. \'5 0) 3 3

4 Name: B o.l(~o.. o\-'oo.~ -= \0 'I. q 2... S~ \2- i~ ---:::.--,qo '{G\ /' ( -\-(; C\i'\ 5 \<. \) 17. A right rectangular pyramid has a base measuring 10 yd by 9 yd. The slant height of the triangular face with the shorter base is 12 yd. The slant heigl.!! of the triangular face with the longer base is 15 yd. What is the surface area of the pyramid? ~ 'S 0::.. \ 5 '4 ~ ltri C\(\9 U L) '\ -i ( O'kl~) CD 348 yd? d. 580 yd? := 3 '-\-6 '"d2-. "T a.120yd 2 c.460yd 2 S'A:.(\O'l.Q) ti(q)(\2-)--i-/.l.\.'7 18. Determine the surface area of a right prism with length 8 ern, width 5 em, and heigh~= ~ C y('i \ L a. 600cm2 Q 132em2 SA =w'n,-\1il'i\","\w -\\w-\\~ -\ f\ b. 480 em- d. 80 em? -= 2. lv.}r\ -\ \ vj --\ \ 'n ) '\ ::: ~ \.5 '"a -\-'6'/..5 -\" ~ 1--?-. J What is the surface area of the right pyramid, to the nearest square millimetre? Sf\:=:::. \2>2.. c..\('('17- SA ~ ~ \c) ~ ~ '0 2- '\. _F;no. s ::. sa ",(g.~ql.\\.q)-t q'l- St\ =-(g. C\'o. ~ f{'2\ "'-.. Sq..\.l(.\«(.. Ii> cts-l a. 279 mm? c. 477 mm? CE)295 mm? d. 891 mm? 20. Which formula can be used to calculate the surface area of a right cylinder? a. SA = 2nr + nr2h c. SA = 2nr + 2nr2h ~ SA = 2nr2 + 2nrh d. SA = nr2h + 2nrh A 21. What is the volume of a right cylinder with radius 1 m and height 3 m, to the nearest tenth of a cubic metre? a. 3.0m3 c. 25.1m3 \j=(c~'(~c\. t::l\. 'oo.~-e.)~'" <f) 9.4 m ' d m 3 = 1\'(' z, v: ~ 6- "\l ~ \. \\~'\..~,c..3) = q. 4 rn 22. Calculate the surface area of a right cylinder with diameter 11.4 em and height 15.6 em, to the nearest square centimetre. ~~1- SA -=- ~ \"\'(' '). -t d-.itr h o 763cm 2 c. 2151cm =-\~~1\ 2 1-5d1-2..)-\-(?~1\~I) t"\ b em- d em-...1 \5,10) S = "ll.o' ~~ ~m r 23. A right cone has diameter 15 m and slant height 12 m. What is its su ace area, to the nearest square metre? C!) 459 m? ~ '-5':,'2- ~ m? SA z: 1\(""2. -\-\\ 'f~ b. 707 m? c- 1-,'5 d m? -=,-\\ '" i.s 2.) -\- ( 1\ "" '1,S t:.. \2..) 24. Which formula is used to determine the volume of a right cone? a. b. cb!~:: ~ I? \.!:;) V = "3 tir: h 4 3 d. V = "3nr = \ l-\- S<\ r<\ 1-\ \I -c,..j... C. (A 'I (LC-'\ b+- ba)-e.) ~h ~ ~ C 1\1".2. " h ') 25. To the nearest cubic metre, determine the volume of a right cone with radius 3 m and height 5.5 m. ~.~;6m~; \j = 3- (\If" 2 ><1-\ ') 4 ~.x,( II -,(~ 2. 'I. 5".'J ) 3.~ ~ 5\,~Y'(\ "~5d- ff''' I

5 -. Name: ~ 26. Calculate the volume of a sphere with radius 2.8 ft, to the nearest cubic foot. a. 23 ft3 c. 69 ft3 b. 33 ft3 (f) 92 ft3 /\ \) ~~ \TX- ~ ~ '= l\ ~\T 'J.. g == d-15~ , To the nearest cubic centimetre, whatis the volume of a sphere with diameter 8 em? -::::\q \:-C\ S\"t- 3 \ a ern? <S> 268 em- \ '(~, 'L-\), _, b. 536 em- d. 67 ern? ~ ::.. ~tn" '"~ '!.) ':' <eol\- = 1~ to '~ CY'0 ~ A can of soup has a radius of 3 em and a height of 10 em. The label on the can covers the entire curved surface of the can. What is the area of the label, to the nearest centimetre? C'I \ \("\0.-(".. ' \)'J e. w C\ (\ta.. 57 ern- c. 245 em? As' ~(. -= ~\\, h ~ 188 ern- d. 283 em- \ -::0- d-'i- \\ t-. 3 t.. \0 =\ \t3~ (J 29. A long, thin cone has a radius of2 em and a height of 15 em. The cone is filled with soft ice cream and then topped with a hemispherical scoop of hard ice cream. Determine the total volume of ice cream, to the nearest cubic centimetre. ~ Sp'n~'(\:.- a. 96 em! c. 71 ern- \j := ~ (Dt\< -\ \j ~<VY\; SP",,{(e. c > 80 em- d. 67 em- '(-::. d-, ~.. z:...l (n'(1.. ~ ~ ') Completion Complete each statement n-; \S C.\)~0 =- ~ ~;2.2.,c;.~ ::. fo~. 'B " 3 3 \I"'~m\~" =.1. -I.. J:l \T:Jf' d- 3 An item that a person might use to approximate a measurement is called a(n) fe.-\-v( e..xl-1-. Nineteen yards is equivalent to S-=t- feet. Q ~ y\~m\sp ~ t\ 'k T\ A 2. ~ -:::.\~#-C6 ~I\(' ~ Twenty feet is equivalent to ~ "'"t V inches. ---'~----- ~ \\'f\1\ l -:.io'j,~-f \ ~ \ ~ To one decimal place, the equivalent of 19 yd is \-=--+_. -=----'"_L-\--'-- m. -= 1q..b ('((\'3 a~~~ 0 ~ Area is measured in S ct='!'- a.v~ units. Volume is measured in -:::\.1>0 C\r0 ~ \ CLAD \ C ---=--lu=n~lts-. ---='3--- -'!...:,""'=-'~bol..-'---=~ e'k;: C. (Y\ ' 6. The surface area of a sphere depends on its C-,---=-~ C=-~ \_U S only. \ 7. The volume of a right cone is '/ 3 of the volume of a with the same radius and height. C'j\\n d\ ey 8. The volume of a right pyramid is \/3 r"sb-i ~'(\S'('(\ with the same base and height. C (){' (e c\' ex.1(\3 U \ Qc?(\-S \'Y\ ") of the volume of a bo~~ Cl(\SvJ.eV-S: os e: COY'feet- 5

6 Name: { Matching Match the correct term to each of the following visuals or descriptions. A term may be used more than once or not at all..i. ~ \\- Y\ -( G. e.c\ apex.../ U\ \ (,\ 'f' f. b. lateral area g. c. right cone h. d. right cylinder i. e. right prism j. r=:">., / right pyramid slant height sphere surface area volume " ,-.. _.,. D 1. \,,- _' _.-~} \6 2. the sum of the areas of all the faces of a three-dimensional object _ S\.A.v:t Ct (-e.. CA -( e j> 4. the amount of space a three-dimensional object occupies \) 0\V\. m0,./~'-~>'" / 'x / " j" ",,'\ 5. ~~ cl 6. A / '\ / \ I. / \.I \! \, I I " L~_-... "';...--;-~, t -.,,) 7. "---,~ 6

7 Name: Short Answer 1. Habib wants to visit his grandfather, who lives 275 mi away. How far does Habib have to travel to see his grandfather, to the nearest kilometre? 2. a) Determine the area of a rectangle that measures 1.5 em by 2.5 em, in square millimetres. /~ b) Determine the area of a rectangle that measures 35 mm by 20 mm, in square metres. 3. What are the surface area and volume of each right cylinder, to the nearest tenth of a unit? a) a cylinder with radius 1 m and height 3.4 m b) a cylinder with radius 7.8 yd and height 2 yd 4. Determine the volume of each object, to the nearest tenth of a cubic unit. a) a right cone with radius 2.2 em and height 6.4 em b) a sphere with radius 5.8 ft Problem ( < 0\ \.1\.\1' on S ) Use the table of conversion factors to help answer the following questions. Imperial Unit SI Unit 1 in em 1 ft m 1 yd ill 1 mi km 1. A unit at Safe Self Storage has length 4.6 m, width 3.1 m, and height 2.4 m. What is the volume of the storage unit, to the nearest cubic foot?.~, 7

8 Name: Determine the volume of a right prism with dimensions 2 ft by 3 ft by 6 ft, to the nearest hundredth of a cubicmetre. 3. Manuel made a kite as shown. He wants to glue gold trim around the perimeter. The trim he wants is sold by the foot. How much gold trim does he need to buy? 100cm\ / '"', I 80 U11 \ L-- --j \\ l \ / /100cm \ I \. / \; 4. A right pyramid fits exactly inside a box in the shape of a right prism. Both objects have the same base and height. If the prism has a volume of 720 cm-, determine the volume of the pyramid. 8

9 9. ANS: B NAT: M3 PTS: 1 DIF: A TOP: Surface Area OBJ: Section 2.2 KEY: lateral area SHORT ANSWER 1. ANS: 275 mi = 275 mi x 1.~1~ mi = km Habib has to travel approximately 443 km. PTS: 0 DIF: A OBJ: Section 1.3 NAT: Ml 1M2 TOP: Converting Between SI and Imperial Systems KEY: conversion I imperial to SI I miles to kilometres 2. ANS: a) The width is 1.5 em or 15 mm. The length is 2.5 ern, or 25 mm. A =lw A = (15)(25) A =375 The area is 375 mm-. b) The length is 35 mm or m. The width is 20 mm, or 0.02 m. A =lw A = (0.035)(0.02) A = The area is m-', PTS: 1 DIP: A TOP: Units of Area and Volume OBJ: Section 2.l NAT: MI KEY: convert within the SI system 4

10 2. ANS: Convert the dimensions to metres. Use 1 ft = m. 2 ft = 2(0.3048) = m 3 ft = 3(0.3048) = m 6 ft = 6(0.3048) = m V=lwh V= (0.6096)(0.9144)(1.8288) V= The volume ofthe prism is approximately 1.02 m'. PTS: 1 DIF: A OBJ: Section 2.1 NAT: M3 TOP: Units of Area and Volume KEY: area I conversion factors I convert imperial to SI I right prism 3. ANS: The kite consists of an isosceles triangle and a semicircle. Determine the circumference of the semicircle. Trd C semicircle = 2" Tr(80) C semicircle = -2- Csemicircle = The circumference of the semicircle is approximately em. So, the perimeter of the kite is approximately , or em. Convert em to feet. Use 1 ft = ern cm = ft The perimeter of the kite is approximately 10.7 ft. Since trim is sold in whole feet, Manuel needs to buy 11 ft of gold trim. PTS: 1 DIF: D OBJ: Section 2.1 NAT: MIl AN3 TOP: Units of Area and Volume KEY: circumference I conversion factors I convert SI to imperial 4. ANS: A right prism has three times the volume of a right pyramid with the same base and height. lum f ld 720 Vo eo pyratm =:3 =240 The volume of the pyramid is 240 em'. PTS: 1 TOP: Volume DIF: B OBJ: Section 2.3 NAT: M3 KEY: calculate volume I problem solving I right prism I right pyramid I SI 7

11 3. ANS: a) SA = 2nr2 + 2nrh SA = 2n(I)2 + 2n(1)(3.4) SA = 2n + 6.8n SA = 8.8n SA = The surface area of the cylinder is approximately 27.6 m", V= nr2h V= n(1)2(3.4) V= The volume of the cylinder is approximately 10.7 m-. b) SA = 2nr2 + 2nrh SA = 2n(7.8)2 + 2n(7.8)(2) SA = n n SA = n SA = The surface area of the cylinder is approximately yd-. V= nr2h V= n(7.8)2(2) V= n V= The volume of the cylinder is approximately yd ', PTS: 1 DIP: B OBJ: Section 2.21 Section 2.3 NAT: M3 1AN3 TOP: Surface Area I Volume KEY: calculate surface area I calculate volume I imperial I right cylinder I SI 5

12 4. ANS: 1 2 a) V= 3nr h 1 2 V = 3n(2.2) (6.4) V = n( ) V = The volume of the cone is approximately 32.4 cm b)v=-nr V = 3n(5.8) V = n ( ) V = The volume of the sphere is approximately ft3. PTS: 1 TOP: Volume DIF: B OBJ: Section 2.3 NAT: M3 I AN3 KEY: calculate volume I imperial I right cone I S1 I sphere "PROBLEM 1. ANS: Convert the dimensions to feet. Use 1 m ~ ft. Length: 4.6 (3.281) ~ The length is approximately ft. Width: 3.1(3.281) ~ The width is approximately ft. Height: 2.4(3.281) ~ The height is approximately ft. Volume of the storage unit: V=lwh V ~ ( )( )(7.8744) V ~ The volume of the storage unit is approximately 1209 ft''. PTS: 1 DIP: A OBJ: Section 2.11 Section 2.3 NAT: MIl M3 TOP: Units of Area and Volume I Volume KEY: area I conversion factors I convert SI to imperial I right prism 6