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## Nuffield Free-Standing Mathematics Activity Volume

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**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.**1 cm**1 mm 1 mm 1 cm 1 mm 1 cm Volume The volume of a shape is the amount of space it fills. 1 m 1mm3 1 m 1 m3 1 cm3 1 m 1 cubic metre**3 cm**2 cm 4 cm Volume of a cuboid Volume = 4 × 2 × 3 Volume = 24 cm3 Volume = length × width × height Volume = area of cross-section x length**Example**60 cm 50 cm 120 cm For a cuboid Volume = length × width × height or Volume = area of cross-section x length Volume of the fish tank Volume = 120 × 50 × 60 = 120 × 3000 cm3 = 360 000 Capacity in litres = 360 000 ÷ 1000 (1 litre = 1000 cm3) = 360 litres**Example Concrete block**10 cm 12 cm 2.5 m For a cuboid Volume = length × width × height or Volume = area of cross-section x length = 250 cm Think about…Why might there be a problem with these dimensions? Volume = 250 × 12 × 10 = 2500 × 12 Volume = 30 000 cm3**20 cm**1.5 m 2 m For a cuboid Volume = length × width × height or Volume = area of cross-section x length Example Sand in sandpit = 0.2m 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).