Volume of a Rectangular Prism
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1 ^hbhi Volume of a Rectangular Prism Quick Review You can use a formula to find the volume of a rectangular prism. The volume is the product of the prism's length, width, and height. Volume = Length x Width X Height This rectangular prism is 7.0 cm long, 3.5 cm wide, and 2.3 cm high. Volume cm X 3.5 cm X 2.3 cm 2.3 cm 3.5 cm = 24.5 cm2 X 2.3 cm 7.0 cm = cm3 The volume of the prism is cm3. TrvTiKSS ; 1 Find the volume of each rectangular prism. a) / T7] h) cm 0.5 cm 3.0 cm 4.0 cm 2.0 cm lol em3 1.2 cm 4 cm3 3o37B cm3 m 144 cm3 102 Bern3 1 o cm3
2 Practice lo Find the volume of each aquarium. a) te) ].0m 60 cm 25 cm 5.0 m 50 cm 20 cm 40 cm 48 cm3 12 m3 37 em3 2. Work with a partner. i) Find 4 small boxes. Label the boxes A, B,C, and D. b) Measure the dimensions of each box. Estimate, then calculate, each volume. Record your results in the table. Sample Answers Box Length Width Height Estimated Welume Actual Volume A 13oS cm 10.3 cm 750 cm cm3 B 9.5 cm 4.0 cm 12.5 cm 73 cm3 475 cm3 C 14o0 cm 8.0 cm ScS cm 750 cm3 728 cm3 D 10 cm 5 cm 10 cm 500 cm3 500 cm3 3. Complete each table. Length WidKJi Height Volume (cm3) Length Width Height Volume (cm3) » Stretch ir T&iiilciiii Jocelyn built a rectangular prism with 36 centimetre cubes. What might be the dimensions of the prism? Give as many answers as you can. 1X1X3 ; 1X2X1 1 x 1 x 1X4X9 1 X X 6; 3 X 2 X 9; 2 X 3 X 6; 3X3X4 103
3 The Cubic Metre / r 'I. - " w A line segment has only one dimension. It is measured using linear units such as centimetres and metres. A flat surface has two dimensions. The area it covers is measured using square units such as square centimetres or square metres. An object has three dimensions. The space it occupies is measured using cybic units such as cubic centimetres or cubic metres. A cube with edge length 1 m has volume one cubic metre, or 1 m3. 1m3 = 100 cm X 100 cm X 100 cm = cm3 1m To find the volume of a rectangular prism in cubic metres, we find the product of the length, width, and height in metres. Volume = 3.0 m X 2.0 m X 2.5 m = 6.0 m2 X 2.5 m = 15.0 m3 The volume of this prism is 15 m3. 3^0 m Tr^ Tfe 1o Would you use a linear, square, or cubic unit to measure? a) area of a desk pad squire umt fe) space in an elevator cubic uino'i> c) length of a pen linear unit d!) perimeter of a dog run Binear unit 104
4 Practies 1 o Find the volume of each box in cubic metres. a) b) 3.0 m 0.5 m 2.1 m 6.0 m 2.0 m 2.0 m 1.5 m I/..0 m 0.5 m 1o5 ms 6o3 m3 2. Name 2 objects whose volume is: Sample Answers a) greater than 1 m3 agn (EB wat rg a cboset b) less than 1 m3 a paoicil box: a tissue box c) about 1 m3 a o]! cirate: a computer box 3o A packing box is a rectangular prism with volume 1 m3. The box is 250 cm long and 100 cm wide. How tall is the box? 40 cm 4o What unit would you use to measure: Sample Answers a) the area of a postage stamp? square millimetre b) the volume of a moving van? cybic metre c) the distance from North Bay, ON, to Vancouver, BC? kilometre Stretch Your Thinking Find the volume of this box in cubic [mi3 10cm 45 cm cm 105
5 y and Volume Quick Review Units of both volume and capacity are used to measure the "size" of three-dimensional objects. Units of volume are used to Units of capacity are used to measure liquids or gases and the containers that hold them. measure the space an object occupies. /A1 Use these relationships to convert between units of volume and capacity: 1 cm3 = 1 ml 1 m3 = 1000 L 1000 cm3 = 1 L 255 cm3 6.7 m3 = 6.7 X 1000 L 1000 L = 6700L = 0255 L i _ 724, 724 L iooo m m3 1c Complete. ) S) OS 75 ml = 7S cm3 b) d) f) 94 cm3 = 9^ ml h) a) 1750 ml = CM oo ooo UEon II )o2 L m3 II on 6 m3 = 4.2 L cm3 = 7 TO mm oil'j 42 cm3 L L cm3 2o How many litres of water would it take to fill a swimming pool 9 m long, 5 m wide, and 2 m deep? L 10
6 Practice 1 c Circle the best estimate of volume or capacity. a) a barrel of water 75 ml (180 L] b) a bowl of porridge 20 L (400 ml c) a moving van 4 m3 150 m3 35 cm3 75 L 2. Selena's rectangular swimming pool holds L of water, a) Find the volume of water in cubic metres. 3i> m3 b) The pool is 2 m deep. How long and how wide might it be? Sample Answer: It could be 6 m Song and 3 m wide. 3o Find the volume of water, in litres, needed to fill each fish tank. 22 cm 60 cm ) 60 cm 45 cm 120 cm 7 40 cm 50 cm cm 2 J I 288 L 195 L 4. Look at a milk carton. Sample Answers How much milk does it contain in litres?. Write this amount in cubic centimetres cm3 In millilitres? Describe how you might find the volume of a golf ball. Sample Answer Pour 250 ml of water into a measuring cup. Add the golf ball. Read the new level to find the volume of the water and the ball. Subtract 250 ml from the new level. Convert the reading to cubic centimetres. Stretch Your Thinking One kilolitre is equal to 1000 L. How many kilolitres of water would it take to fill a pool 9 m x 6 m x 2 m? 108 kilolitres 107
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