# 2.5 Measuring capacity

The basic metric unit for capacity is the litre, usually denoted by the symbol l (though sometimes an uppercase L is used to avoid confusion with the number 1).

In the SI system, units such as cubic metres (m^{3}), cubic centimetres (cm^{3}) and cubic millimetres (mm^{3}) are used. These two systems are linked because:

1 ml = 1 cm

^{3}

The animation below illustrates how to convert between the most commonly used units of capacity:

Notice that to convert cubic centimetres to cubic millimetres, you need to multiply by 1000, NOT 10. To see this, imagine that you have a box which has internal measurements 1 cm by 1 cm by 1 cm. So, its volume is 1 cubic centimetre.

Now imagine filling it with tiny cubes, each side of which was 1 mm, so the volume of each tiny cube is 1 mm^{3}. You would be able to fit 10 rows each with 10 tiny cubes in the bottom of the box, that is 100 tiny cubes altogether.

But these cubes would only fill the depth of the box to 1 mm. So you would be able to get 10 layers (each with 100 tiny cubes) into the box overall.

So there would be 1000 tiny cubes in the box.

In other words 1 cm^{3} = 1000 mm^{3}.

Can you explain why 1 m^{3} = 1 000 000 cm^{3}?

The argument is similar to that above for cm^{3} and mm^{3}, except that there are 100 cm in a m, so a cubic metre (a 1 m by 1 m by 1 m cube) has 100 by 100 by 100 little cubic cm in it.

## Example 9

Convert 500 cm^{3} into litres.

### Answer

To convert 500 cm^{3} into l, divide by 10 to convert into cl, and then divide by 100 to convert the measurement into l.

So, 500 cm^{3} = 500 ÷ 10 cl = 50 cl = 50 ÷ 100 l = 0.5 l.

Try some yourself – use the calculator to type in the amount and then choose the units you want to convert. Then choose the operation (multiply or divide) and the factor. Then select check to see if your answer is correct.