# 1.4 Cubes

To find the cube of a number, multiply three copies of it together. For example:

You can use your calculator to find cubes. 2^{3} is ‘two cubed’ or ‘two to the power three’. Just as ‘square root’ is the opposite process to squaring, so 'cube root' is the opposite process to cubing.

4^{3} = 64, so = 4.

In the same way that square units are used to measure area, cubic units are used to measure volume. A cube measuring 1 cm × 1 cm × 1 cm has a volume of 1 centimetre cubed, or 1 cubic centimetre, written as 1 cm^{3}, or 1 cc. The volume of a ‘box’ is length x width x height, so the volume of this cube (10 mm × 10 mm × 10 mm) in millimetres is

1 cm^{3} = 10 mm × 10 mm × 10 mm = 1000 mm^{3}.

## Example 5

My half-litre measuring jug is marked off in divisions of 100 ml, with subdivisions of 20 ml. I want to measure out 420 cc, but the only conversion table I have tells me that a litre is one cubic decimetre. (One decimetre is a tenth of a metre.) How many cubic centimetres are there in a litre? Can I use the measuring jug for 420 cc?

### Answer

There is one cubic decimetre in a litre, so 1 litre measures 1 dm × 1 dm × 1 dm (if shaped into a cube). (Note: 1 m = 10 dm = 100 cm.) There are 10 centimetres in a decimetre, so a 1 litre cube would measure

10 cm × 10 cm × 10 cm = 1000 cm^{3}.

So 1 litre is 1000 cm^{3}. This is a useful result.

But there are 1000 millilitres in a litre, so it turns out that a millilitre is the same as a cubic centimetre.

1 ml = 1 cm^{3}.

So I can use the jug to measure 420 ml, or 420 cc (or cm^{3}).

(Note: 1 cubic centimetre can be written as 1 cc or 1 cm^{3}.)