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5 Volume

Volume is the measure of the amount of space inside of a solid (3D) object. The volume of a cube or cuboid is measured by multiplying length by width by height. It is always measured in cubic units, such as mm3, cm3, m3, etc.

Example: Volume of a cuboid

What is the volume of a box with a length of 8 cm, a width of 4 cm and a height of 2 cm?

Figure 27 A box

Method

The volume is:

Extract

8 cm × 4 cm × 2 cm

You can also write this as:

Extract

32 cm (8 cm × 4 cm) × 2 cm = 64 cm3

Watch the following clip for some more examples:

Now try the following activity.

Activity 11: Calculating volume

  1. Calculate the volumes of the following:

Hint: As with perimeter and area, you may need to convert to make the units the same.

Length Width Height Volume
6 m 2 m 3 m
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10 mm 10 mm 10 mm
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36 mm 2 cm 4 cm
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9 m 2 m 180 cm
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  1. A children’s sandpit is 1 m wide and 1.5 m long. What volume of sand would be needed to fill the sandpit to a depth of 10 cm? (Note that depth is the same as height but measured in a downward direction.)
  2. David has built a log store that measures 2 m × 1 m × 1 m. He wants to order some logs ready for the winter. The local supplier only delivers logs in 1.5 m3 loads. Will David’s store be big enough to hold one load?

Answer

  1. The answer is as follows:

Length Width Height Volume
6 m 2 m 3 m 36 m3
10 mm 10 mm 10 mm 1 000 mm3
36 mm (convert to 3.6 cm) 2 cm 4 cm 28.8 cm3
9 m 2 m 180 cm (convert to 1.8 m) 32.4 m3
  1. First you need to convert 10 cm to metres – it’s 0.1 m. Then you can calculate area:
    • 1 m × 1.5 m × 0.1 m = 0.15 m3
  2. The volume of David’s store is 2 m × 1 m × 1 m = 2 m3, so it will be big enough to hold one load of the logs.

Summary

In this section you have calculated the volume of cubes and cuboids.

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