Name: Block: Date: AWM1O Ch.3 Getting Started Notes

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1 Name: Block: Date: AWM1O Ch.3 Getting Started Notes We are going to be working on length, area and volume problems in chapter 3, but first we are going to review some skills you should know that are important to remember for this chapter. PERIMETER (P): the distance around a shape, you can calculate this by adding up all the sides of a shape (For Circles the formula is C=2Trr or C=nd where r=radius and d=diameter) Ex. 9 Perimeter = w = (2x9) + (2x4) =26 Perimeter= add up all sides = = 30 cm 9 crri 13 crri 3 crri CIRc.T..JMFERENCE (C): the distance around a circle (perimeter of a circle!) - need the radius (half distance across a circle) or diameter (full distance across a circle) to find it! - formulas are on your formula sheet C = 2rtr and C = Ex. circumference = 2Ttr = 2(3.14) (3) = cm

2 Finding the Perimeter: Ex. 1) Find the perimeter of the shape shown here. ZBcm Hint: start at one side and work your way around in order so you don t miss any sides P = P = 20.3cm 22cm 2i cm 21J Ex. 2) Find the missing side lengths and the perimeter for the shape below. E=4+2=6km F=1+1=2km E Perimeter = = 16km 2 km Finding the Circumference: Ex. 3) Find the circumference of the cirde shown below. (remember rt about 3.14) is F C = 2nr = 2 x 3.14 x 6 (or even better - instead of 3.14 use the 11 button on your calculator!) C = 3 7.7cm (don t forget the units!) Ex. 4) Find the circumference of a circle with diameter 8.5m C zndnx8.5 C = 26.7m

3 Area = the amount of space inside a figure (units are always squared eg. cm2) Area Formulas Rectangle: area = length times width = L x W Triangle: area = one half base times height = 1/2 b x h Circle: area 2 pi r squared (also know as it x r x r) = irr Area of a triangle: Area = ½ b x h =½(5x6) =O.5x5x6 = 15 cm2 5 Area of a Circle: 2 = (however since they gave us diameter we Area = irr need to calculate radius r = ½ d so if d=14 then radius is ½ that or r=7) Area = rtr 2 = 3.14 (7)2 = 3.14x7x7 2 = inches How to solve an equation: Add/subtract to isolate the variable (letter) then divide by the number in front of the variable 12 3P = (Add 12 to each side to get 3p by itself) 12+3p = 3 = 15 (Now divide each side by 3) 3p = 1. p=5 Order of operations (BEDMAS): brackets, exponents, division, multiplication, addition, subtraction: 5+ 4(53)3 (brackets first 5-3 = 2) 5+ 4(2)3 (exponents next (2)3 means 2x2x2 = 8) 5+ 4(8) (multiplication next so 4x8 = 32) 5+32 (finally the addition) 37 (final answer)

4 Name: Block: Date: AWM1O Ch. 3.1 Systems of Measurement Notes There are two major systems for measurements: the Systeme International (SI) and the imperial system. In Canada we use the SI system most of the time, but it is still important to know the imperial system and to be able to convert between the two systems! The SI uses measurements that are multiples of 10 so it is an easier system to work with. SYSTEME INTERNATIONAL (SI): measurement system based on multiples of 10 Ex. Centimetres, metres, litres, etc. - like the metric system! IMPERIAL SYSTEM: measurements system used in the US and trades areas - not a common value to multiply by to convert between the units - use your formula pages to look up conversions Ex. feet, inches, yards, miles,etc. CONVERSiOu FACTORS: fraction that has equal values on the top and bottom used to convert from one unit of measurement to another Ex. 12 inches (12 in = 1 foot so if you divide these they equal 1!) 1 foot Common imperial Conversions: 12 inches (in or ) = 1 foot (ft or ) 36 inches = 1 yard (yd) 3 feet = 1 yard 5280 feet = 1 mile (mi) 1760 yards 1 mile Converting between Imperial Untis: Ex. 1) a) Convert 3 yards to feet. 3 yards x 3 feet = 9 feet 1 yard c) Convert 47 inches to feet and inches. 47 inches x 1 foot = = 12 inches 12 j b) Convert 3 yards to inches. 3 yards x 3 feet x 12 in = 108 inches lyard ifoot d) Convert 47 inches to yards. 47 in x 1 ft xj= 4.7. = 1.31 yards l2in 3ft inches is 3 feet and 11 inches

5 Ex. 2) Jessica is building a pen for the baby chickens. The perimeter of the pen will be 197 inches. a) What will the perimeter of the enclosure be in feet and inches inches x 1 foot = 19.2 = inches = 16 feet 5 inches is the perimeter of the pen. b) The wire mesh is sold by the foot. It costs $1.88/ft. What will be the cost of the materials before taxes? Need 17 feet to have enough if it is sold by the foot! 17 feet x $1.88 foot = $31.96 It will cost $31.96 to buy the wire mesh. 1 foot Ex. 3) The school leadership class has 6 yards of fabric that will be cut into strips 5 inches wide to make decorative banners for the school dance. How many banners can be made? 6 yards x 3 feet x 12 inches = 216 inches 1 yard 1 foot 216 inches = 43.2 The leadership class can make 43 complete banners. 5 inches Ex. 4) Wilhelmina, a seamstress, is sewing bridesmaids dresses. She orders the fabric from the United States, where fabric is measured in yards. Each dress requires 3yards of silk, i)/ yards of lace fabric, and 7)4 yards of trim. How much of each type of material does Wilhelmina need to make 5 dresses? Easy trick! Use Decimals!!!! Silk: 3.5 yards x 5 = 17.5 yards (17)4 yards or 17 yards 6 inches) Lace: 1.5 x 5 = 7.5 yards (7)4 yards or 7 yards 6 inches) Trim: 7.25 x 5 = yards(36 )/ 4yards or 36 yards 3 inches)

6 Ex. 5) How much baseboard is needed to finish the room shown below. Find the perimeter! Add the feet then add the inches and convert! Total Feet = 5, Subtract the doorway feet = Total inches = = 138 Subtract the doorway inches = = 132 l32inxlfoot= 132= lift l2in 12 Total Distance = 42 + ii = 53 You would need 53 feet of baseboard to finish the room. Assignment: Ch. 3.1 Assignment

7 Name: Block: Date: AWM1O Ch. 3.2 Imperial and SI Conversions Notes When dealing with measurements it is important to be able to find the area of objects you are measuring. We will review how to find the area of rectangles, circles and triangles and also how to work backwards to find measurements from the area of an object. AREA: the size of a surface (like the size of our floor in the classroom) - has square units, ex. m2 (square matres), ft 2 (square feet) Important area formulas: (also see your data booklet!) A fw Area of a rectangle, where is the length and w is the width, A nr Area of a circle, where r is the radius and a is the constant, p1. A - bh Area of a triangle, where b is the length of the base and Ii is the height, A ru s Area of the surface of a cone, where r is the radhis and s is the slant height. It is also important to be able to convert SI units to imperial units. We will use conversion factors, just like in Ch. 3.1, to convert one unit to another unit. Here are the common conversions for imperial to SI units. lin=2.54cm lyd=0.915m lft=30.scm lmi=1.6km 1 ft= m Using Area: Ex. 1) A rectangular classroom has dimensions of 16ft by 25 ft. What is the area of the classroom? Arearectangie Lw = 16ft x 25ft = 400ft 2 (ft x ft = ft 2...watch your units with area!) The area of the classroom is 400 ft 2. Ex. 2) Sumo is a traditional Japanese martial art. The area of a circular sumo ring, or dohyoi, is m2. What is the radius of the ring? A nra 16,28 rn 2 Ii?Lr 128 r Divide both s des by a to isolate The radius of a sumo rinu is 228 m.

8 Converting between Imperial and SI Untis Ex 3) Mary is delivering a load of goods from Vancouver, BC, to Seattle, WA, then in Seattle, she is picking up another load to deliver to Albuquerque, NM The distance from Vancouver to Seattle is 220 km and the distance from Seattle to Albuquerque is 1456 mi The odometer in Mary s truck records distance in kilometres a) What is the total distance she will travel, in kflometres (Remember you can t add distances if they don t have the same units 1) 1 456m1 x 1.6 km = 2330 km Find the distance in kilometres from Seattle to I ml Albuquerque 220 km km = 2550 km Add the two distances to find the total distance. Mary will travel about 2550km. b) If her odometer read km when she left Seattle, what did it read when she left Vancouver? = Subtract the distance she travelled from the odometer reading. Her odometer read when she left Vancouver c) What will her odometer read when she reaches Albuquerque? = Add the distance from Seattle to Albuquerque to the odometer reading. Her odometer should read about when she reaches Albuquerque. Ex, 4) Rebecca is planning to install sod in her backyard, which is m by 9.8 m. If sod costs $0.28/ft 2, how much will it cost to sod the backyard? Note you must change to the units you want before finding the area! m x I ft = ft Change the measurements of the backyard to feet m 9.8mx Ift =32.13ft m Her yard is ft long and ft wide.

9 A = Lw Calculate the area of her backyard. The area of a A = x rectangle is calculated by multiplying the length by A = ft 2 the width. She will need approximately square feet of sod at $0.28/ft ft x $0.28 = $ It will cost about $ to sod her backyard. ift

10 Name:.3 Block: Date: A+W Math 10 Ch. 3.3 Surface Area Notes SURFACE AREA: the area on the outside of a 3-dimensional (3-D) object GEOMETRIC NET: the unfolded and flattened picture of a 3-D object. - drawing this picture can help us find the surface area Finding Surface Area of a Cylinder: Ex. 1) A cylindrical poster tube is 56 inches tall and 8 inches in diameter. What is its surface area in square inches? Cvindr sw = 2th - SA=2rrr 2+2tth Net Shape / IC2rr-, - 2 Finding Surface Area of a Cone: Ex. 2) You must make a conical funnel out of sheet metal. If the funnel is 9 inches tall, has a slant height of 10.7 inches, and has a radius of 5.8 inches at the top, what is the surface area of the sheet metal in square feet? 5,,9cS toc irrs / I I h\ = (c2 + Net Shape -

11 Finding Surface Area of a Suhere: Ex. 3) The diameter of a baseball is 3m. What is the surface area in squared centimetres? Sphere SA4tr 2 or SA = 2 M.Ejnding Surface Area of a Square-Based Pyramid: Ex. 4) You are making a mini version of one of the ancient Egyptian pyramids. Your pyramid is 12cm high and the base sides are both 10cm long. What is the surface area of your pyramid? Square-13iscd Pyramid ( ) /7 IhF\ 4b - Sit = 2bs+fr \ 2 Einling Surface Area of a Rectangular Prism: Ex. 4) You have been hired to paint the exterior of a storage bin. If the bin is a rectangular prism that measures 2.3 yards by 4.4 yards by 2.8 yards, what is the surfacearea of the bin? RccanguIar Prism Sit = wh + wh + 1w- 1w + Ui + Ui Sit = 2(wii+Iw lh) 5c5 Z3Z- C) Z) Assignrnen: Ch. 3.3 Assignment

12 Name: Block: Date: AWM1O Ch Volume Notes The SI unit for measuring volume is the litre but the imperial unit for volume is the pint. However, volume can also be measured in millilitres, cubic metres, cubic inches, cubic feet or many others. Especially in cooking, or other activities that use liquid measurements, it is important to be able to convert between different units of volume. VOLUME: the amount of space an object takes up volume of a rectangular prism (box) = length x height x width = lw h - units are cubed ex. in3 CAPACITY: the maximum amount a container can hold ie. the amount of volume inside an object Some Conversions to note: 4 quarts = I US gallon 1 cup = 250 rnl 2 pints = 1 quart 2 cups = 1 pint Finding the volume of a rectangular prism Ibox): 1 teaspoon (tsp) = 5 milli[itres (ml) 1 tablespoon (tbsp) = 1 5 rnl 1 cup = 250 ml 1 litre = 0.26 US gallons Ex. 1) What is the volume of a packing box that measures 10cm by 5cm by 3cm? V = iwh V= 10cm 5cm 3cm Write the formula for volume. Put in the side lengths. V= 150 cm3 The volume of the box is 150cm 3. Ex. 2) Alfred has a bulk container that holds 2000 cubic inches of dog biscuits. He plans to sell the biscuits in small boxes that measure 5 by 8 by 6. How many boxes will he need to sell all the dog biscuits? V=t wh v= V = 240 in3 (or cu in) 2000 = Alfred would need 9 small boxes. Write the formula for volume. Put in the side lengths for the small box. Divide the volume of the larger box by the volume of the smaller box Round up, so that all of the biscuits fit in boxes.

13 Converting between Units of Volume: Ex. 3) You are travelling through the US and your car s gas tank has a capacity of 55 litres. a) How much is this in American gallons? 55L x 0.26 us gallons = 14.3 US gallons IL Your car can hold 14.3 US gallons of fuel. b) How much is this in British gallons? 1 British gallon = 6/5 US gallon (6/5 = 1.2) 14.3 US gallons xl British gallon = 11.9 British gallons 1.2 US gallons Your car can hold 11.9 British gallons of fuel. Ex. 4) You are opening a French bakery and want to make authentic French recipes. All the recipes are given in metric units, but you have imperial measuring devices. The crème brulée recipe requires 500 ml of cream and 1.25 ml of vanilla. a) How much cream will you need, in cups? Convert 500 ml to cups. 500mLx I cup = 2 cups 250mL You will need 2 cups of cream. b) How much vanilla will you need, in teaspoons? Convert 1.25 ml to teaspoons. 1.25mLx I ts = 0.25 tsp (or 1/4 tsp) 5m L You will need ¼ tsp of vanilla. c) How much cream will you need, in fluid ounces? (1 fi oz = 30 mu Convert 500 mu to fluid ounces. 500mLx I floz = l6floz 30m L You will need 16 fi oz of cream.