© 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).