Year 8 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.

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.

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:

#### Example 1

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

a.

b.