© Nuffield Foundation 2011

Nuffield Free-Standing Mathematics Activity

Volume

Volume

The containers for these products are all cuboids.

This activity is about finding the volume of a variety of cuboids like these.

Companies need to know how much containers like these can hold.

1 cm

1 cm

1 cm 1 mm

1 mm

1 mm

The volume of a shape is the amount of space it fills.

1 m

1 cubic metre

1 m3 1mm3

1 m

1 m

1 cm3

Volume

Volume = length × width × height

Volume = 4 × 2 × 3

4 cm

3 cm

2 cm

Volume = 24 cm3

Volume = area of cross-section x length

Volume of a cuboid

For a cuboid Volume = length × width × height

or Volume = area of cross-section x length

Volume of the fish tankExample

60 cm

120 cm50 cm

Volume = 120 × 50 × 60

= 120 × 3000

= 360 000 cm3

Capacity in litres = 360 000 ÷ 1000

= 360 litres(1 litre = 1000 cm3)

Example Concrete block

10 cm

2.5 m12 cm

Volume = 250 × 12 × 10

= 2500 × 12

Volume = 30 000 cm3

= 250 cm

For a cuboid Volume = length × width × height

or Volume = area of cross-section x length

Think about…Think about…Why might there be a problem with these dimensions?

Volume = 0.6 m3

Example Sand in sandpit

20 cm

2 m1.5 m

Volume = 2 × 1.5 × 0.2

= 3 × 0.2

= 0.2m

= 0.6

For a cuboid Volume = length × width × height

or Volume = area of cross-section x length

Think about…Think about…Which dimension should be converted?

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?

Volume

Suggest dimensions that you could use to make a carton with a volume of 1 litre (1000 cm³).