1. Nuffield Free-Standing Mathematics Activity
Volume

2. 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.

3. 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

4. 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

5. 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 =
cm3
Capacity in litres
= ÷ 1000
(1 litre = 1000 cm3)
= 360 litres

6. 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 =
cm3

7. 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

8. 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).