Nuffield Free-Standing Mathematics Activity Volume

Volume The containers for these products are all cuboids. Companies need to know how much containers like these can hold. This activity is about finding the volume of a variety of cuboids like these.

Volume The volume of a shape is the amount of space it fills. 1 m 1 cm 1 mm 1 m 1mm3 1 m3 1 cm3 1 m 1 cubic metre

Volume of a cuboid Volume = 4 × 2 × 3 Volume = 24 cm3 3 cm 2 cm 4 cm Volume = length × width × height Volume = area of cross-section x length

For a cuboid Volume = length × width × height or Volume = area of cross-section x length Example 60 cm 120 cm 50 cm Volume of the fish tank Volume = 120 × 50 × 60 = 120 × 3000 = 360 000 cm3 Capacity in litres = 360 000 ÷ 1000 (1 litre = 1000 cm3) = 360 litres

For a cuboid Volume = length × width × height or Volume = area of cross-section x length Example Concrete block 10 cm 2.5 m 12 cm = 250 cm Think about… Why might there be a problem with these dimensions? Volume = 250 × 12 × 10 = 2500 × 12 Volume = 30 000 cm3

For a cuboid Volume = length × width × height or Volume = area of cross-section x length Example Sand in sandpit 20 cm = 0.2m 1.5 m 2 m Think about… Which dimension should be converted? Volume = 2 × 1.5 × 0.2 = 3 × 0.2 = 0.6 Volume = 0.6 m3

Volume Reflect on your work 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 that you could use to make a carton with a volume of 1 litre (1000 cm³).