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Year 7 Interactive Maths - Second Edition


Volume

Volume is the amount of space that a three-dimensional object occupies; and it is measured in cubic units.  The most commonly used units of volume are:
  • mm3 - millimetres cubed
  • cm3 - centimetres cubed
  • m3 - metres cubed

The diagram of a cubic centimetre is shown below.

1 cubic centimetre

Dotted lines represent the edges of the cube that can not be seen when we look at it from this angle.  Each face of the cube is a square centimetre, so the cube is said to be a cubic centimetre.


Finding Volume by Counting the Number of Cubes

If we can divide a three-dimensional object into small cubes of side-length 1 cm as shown below, then the volume of the object can be found by counting the number of cubes or cubic centimetres.

3 layers of 2 rows of 6 cubes

For example, the top layer of cubes in the rectangular box shown above has two rows of 6 cubes.  So, there are 12 cubes in the top layer.

Since there are 3 of these layers:

Volume is 36 cubic centimetres


Example 1

Find the volume of each of the following solids by counting cubes.  Note that each small cube represents 1 cm3.

a.

1 layer of 2 rows of 6 cubes

b.

4 layers of 2 rows of 5 cubes

Solution:

Volume of the solid is 12 cubic centimetres

Volume of the solid is 40 cubic centimetres


Key Terms

volume, three-dimensional, cubic units, millimetres cubed, centimetres cubed, metres cubed


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