1 cm 3. 1 cm. 1 cubic centimetre. height or Volume = area of cross-section length length
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1 Volume Many things are made in the shape of a cuboid, such as drink cartons and cereal boxes. This activity is about finding the volumes of cuboids. Information sheet The volume of an object is the amount of space it fills. Large volumes are measured in cubic metres (m 3 ). Smaller volumes are measured in cubic centimetres (cm 3 ) or cubic millimetres (mm 3 ). 1 cm m 3 1 cm 1 cm 3 m m 3 1 cubic metre 1 cm 1 cubic centimetre m 1 cubic millimetre In this cuboid there are 3 layers of cubes. There are 2 rows of 4 cubes in each layer. 3 cm The total number of cubes = The volume of the cuboid = = 24 cm 3 4 cm 2 cm For any cuboid: Volume = length width height height or Volume = area of cross-section length length width The volume of liquids is usually measured in litres or millilitres. 1 litre = 1000 ml and l = 1 cm 3 1 litre = 1000 cm 3 and 3 = 1000 litres Nuffield Free-Standing Mathematics Activity Volume Student sheets Copiable page 1 of 6
2 Fish tank example Volume of fish tank = = = cm 3 60 cm Volume of fish tank = 360 litres. (Check the calculation on your calculator.) 50 cm 120 cm Note the volume of a container for liquids is often called its capacity. It is important that all the dimensions of the cuboid are in the same units. Concrete block example Find the volume of a concrete block that is 2.5 metres long, 12 centimetres wide and 10 centimetres high. 2.5 m = 250 cm 10 cm 12 cm Two of the dimensions, the width and height, are in centimetres. = 100 cm Converting the length to centimetres: 2.5 m = = 250 cm Volume of concrete block = = Volume of concrete block = cm 3 (Check the calculation on your calculator.) Sand pit example A sand pit is 2 metres long and 1.5 metres wide. How much sand will it take to fill the sandpit to a depth of 20 centimetres? In this case, two of the dimensions, the length and width, are in metres. Converting the height to metres: 20 cm = = 0.2 m Volume of sand needed = = Volume of sand needed = 0.6 m 3 (Check the calculation on your calculator.) 2 m 1.5 m 20 cm = 0.2 m Nuffield Free-Standing Mathematics Activity Volume Student sheets Copiable page 2 of 6
3 Try these Work out your answer for each question in the box. 1 A heating engineer needs to work out the volume of this room. 3 m 5 m 3 m 2 All the edges of this dice are 10 mm long. 10 mm 10 mm 10 mm 3 A brick is 20 cm long, 12 cm wide and 10 cm high. 20 cm 10 cm 12 cm Nuffield Free-Standing Mathematics Activity Volume Student sheets Copiable page 3 of 6
4 4 A storage box is 1.5 m long, 1.2 m wide and high. Find its volume. 1.2 m storage box 1.5 m 5 The picture shows a block of cheese. 8 cm 15 cm 4 cm 6 The picture shows the dimensions of a fish tank. Find its volume (capacity) in cubic metres. 0.8 m 1.5 m 7 The diagram shows the dimensions of a waste disposal container. 2.4 m 3.5 m 2.0 m Nuffield Free-Standing Mathematics Activity Volume Student sheets Copiable page 4 of 6
5 8 A stock cube is 20 mm long, 20 mm wide and 20 mm high. Calculate its volume. 20 mm 20 mm 20 mm 9 A carton of orange juice measures 9 cm by 6 cm by 19.5 cm. Show that its volume is just over 1 litre. 10 A rectangular swimming pool is 25 m long and 10 m wide. How many litres of water do you need to fill it to a depth of 2 m? 25 m 10 m 2 m 11 Ice-cream mixture is poured into a container to make a block of ice-cream 20 cm long, 8 cm wide and 5 cm high. a Find the volume of the block. 5 cm b How many blocks can you make with 4 litres of ice-cream mixture? Ice-cream 20 cm 8 cm Nuffield Free-Standing Mathematics Activity Volume Student sheets Copiable page 5 of 6
6 12 A builder plans a tarmac drive for a new house. The drive is in the shape of a rectangle 12 metres long and 3 metres wide. The tarmac needs to be 20 cm thick. What volume of tarmac does the builder need? 13 A rectangular paddling pool is 2.5 m long and 2 m wide. How many litres of water do you need to fill it to a depth of 40 cm? 14 What volume of concrete is needed for a path which is 80 metres long, 1.5 metres wide and 150 mm deep? At the end of the activity A manufacturer needs to know the volume of a box (cuboid). Explain how to find this. What units can volume be measured in? Suggest dimensions you could use to make a carton with a volume of 1 litre (1000 cm³). Nuffield Free-Standing Mathematics Activity Volume Student sheets Copiable page 6 of 6
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