Chapter 6. Volume. Volume by Counting Cubes. Exercise cm 3. The volume of a shape is the amount of space it takes up.
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1 Chapter 6 Volume Volume by Counting Cubes The volume of a shape is the amount of space it takes up. 3 The basic unit of volume is the cubic centimetre. A small cube which measures by by is said to have a volume of 1 cubic centimetre and is written as 3. Exercise How many centimetre cubes does this shape contain? 3. By counting the number of cubes on the top face, calculate and write down the volume of each of the shapes in cubic centimetres (cm 3 ). Copy and complete :- It s volume is... cm Write down the volumes of each of these shapes. Each small cube has a volume of 3. (e) (f) (e) (f) (g) (h) (g) (h) Chapter six page 45 Volume
2 Volume - Cubes & Cuboids - a Formula Look at the cuboid on the right and find out if we can determine its volume without having to count it cube by cube. The top layer consists of 4 rows of 3 cubes => 4 x 3 (= 3 ) There are 2 identical layers => Volume = 2 x (4 x 3) (= 2 3 ) This means a simple process to determine the volume of a cuboid (or cube) is to multiply the 3 dimensions. Volume = length x breadth x height or in symbols V = L x B x H Exercise Copy and complete :- 3. Vol = L x B x H 2. Use the above formula to calculate the volumes of these cuboids :- (Show 3 steps each time). V = 6 x 2 x 3 V =... cm 3 (e) (f) 4. The same formula can be used to calculate the volume of a cube. In a cube, all of the edges are the same length. Copy and complete :- Vol = L x B x H V = 7 x 7 x 7 V =... cm 3 (Check each answer by counting cubes). 3. Use the above formula to calculate the volume of each of these cuboids :- 5. Calculate the volume of each of these cubes :- 1 Chapter six page 46 Volume 3
3 6. This shape consists of a blue cuboid on top of a pink one. Copy and complete :- Volume (blue) Volume (red) = L x B x H = 5 x 4 x 3 =... cm 3 = L x B x H = 7 x 6 x 3 =... cm 3 Total Volume = =... cm 3 9. Find the volumes of these shapes : Repeat for this shape consisting of a yellow and a green cuboid Find the volumes of these shapes consisting of 2 or more cuboids :- 10. Look at the yellow cuboid. It s volume is known to be 3 3. How many cubes are there on the top layer? h cm Calculate what the height (h cm) of the cuboid must be. 11. Calculate the H, L or B in these cuboids :- H cm Volume = 80 cm 3. H cm Volume = B cm Volume = 960 cm 3. Volume = 3600 cm 3. (e) (f) A cube. (hard!) H cm 1 1 Volume = 1500 cm 3. Volume = Chapter six page 47 Volume
4 Volumes of Liquids - Capacity When talking about the volumes of liquids, we do NOT talk about buying 56 3 of milk, or drinking a 330 cm 3 bottle of beer. Look at this hollow cube with sides long. If we fill it with water, it will hold 3. When discussing liquids, we refer to this as 1 millilitre. 3 = 1 millilitre = 1 ml So a carton of milk might hold 567 ml and a bottle of raspberry juice 330 ml. Look at this carton, measuring by by. Its volume is given by :- V = L x B x H = 10 x 10 x 10 = 1000 cm 3. If filled with water, we say its CAPACITY is 1000 ml or 1 litre. Exercise Calculate the volume of this cuboid in cm This metal tank is to be filled to the top with oil. If it is filled with water, how many millilitres will it hold? 2. Calculate the capacity of each of these containers when full of liquid : cm Calculate its volume in cm 3. How many millilitres of oil will it hold? What is its capacity in litres? 4. How many litres of oil will each of these tanks hold when full? cm 50 cm 1 70 cm cm cm 50 cm 1 Chapter six page 48 Volume
5 5. Remember : to change from:- millilitres > litres you simply Change each of the following to litres : 4000 ml 8000 ml ml 6500 ml (e) 1200 ml (f) ml (g) 700 ml (h) 200 ml (i) 15 ml. 6. Remember : to change from:- litres > millilitres you simply x Change each of the following to millilitres : 5 litres 9 litres 17 litres 8 5 litres (e) 2 3 litres (f) 19 5 litres (g) 0 4 litres (h) 0 35 litres (i) 0 08 litres. 10. This little ingot of gold is in the shape of a cube of side 0. Calculate its volume in cm 3. How many ingots like this must be melted down to make this gold bar? 6 What will the total weight of the bar be if 3 of gold weighs 19 3 grams? 11. This tank is half full of water This lead-lined box is used to store liquid radioactive waste. How many litres of waste can it hold when full? 4 30 cm 60 cm 50 cm 8. This bucket holds 4 8 litres when full. How many millilitres is this? The shallow plastic tray is used to fill the bucket with water. Calculate its volume in cm 3. How many millilitres will the tray hold? How many times will the tray have to be used to fill the bucket to the top? 9. Davie buys a slab of pink plasticine. 1 1 Calculate how many litres of water are in the tank. When the tap is opened, water pours out at the rate of 12 litres per minute. How long will it take for the tank to empty? 12. This fish tank has a base measuring 5 by 40 cm. 44 litres of water is poured into? cm the tank. How many millilitres of water is this? To what depth will the water fill the tank? 13. This 5 litre jug of water is poured into this tank cm 30 cm He cuts pieces off to form small cubes with sides. 1 By calculating the volume of both the slab and the cube, find how many cubes he can make. 30 cm Will the tank overflow? (explain). Chapter six page 49 Volume
6 1. Write down the volumes of each shape (Each small cube is 3 ). 5. Calculate the total volume of this shape : How many cubes are there in the top layer of this shape? How many layers are there? What is the volume of the whole shape? 3. Calculate the volumes of the following cuboids using the standard formula This yellow metal block has a hole running from top to bottom. 2 Calculate the volume of metal used to make it. 7. Calculate the volume of this tank in cm 3. How many litres of water will it hold? 40 cm 1 60 cm 8. What is the maximum capacity of this tray? cm m (careful!) 2 4. The volume of this cuboid is h cm 9. This water tank holds 36 litres of water. How many times can a small plastic container measuring by 1 by be filled from the tank? 1 1 Given that its length is 1 and its breadth is 1, calculate its height. 1 Chapter six page 50 Volume
1 cm 3. 1 cm. 1 cubic centimetre. height or Volume = area of cross-section length length
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