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Succeed with maths: part 2
Succeed with maths: part 2

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3 Volume

Here the units that are used in everyday life differ from the SI units for volume. In the SI, units of volume are based upon the metre, with a cubic metre being standard. However, this is a very large volume and not of much use to us when measuring everyday objects. To get an idea of how large 1 cubic metre is, imagine a box that is 1 metre high by 1 metre wide by 1 metre long – that is 1 cubic metre and would be a lot of milk!

The base unit for volume that is used in everyday situations is the litre (abbreviated as ‘l’ – lower case ‘L’, not upper case ‘i'). This is from the metric system of measurement on which the SI is based. Adding the prefixes as before gives us the related units of millilitre (ml) and centilitre (cl). Note this could also be continued to include a kilolitre, but larger volumes are usually measured in cubic metres, where 1 cubic metre is the same as 1000 litres (or a kilolitre).

Again, using the knowledge of prefixes it can be deduced that a millilitre is a thousandth of a litre, and a centilitre is a hundredth of a litre. From this the following can be stated:

  • 1 litre = 1000 ml
  • 1 litre = 100 cl.

These relationships can also be displayed in a diagram, showing how to convert between the different units, as shown below:

A figure showing how to convert from litres, to centilitres, to millilitres.
Figure 1 Converting between units of volume

Now you’ve had lots of practice with converting between units, see how you get on with this next activity. Think back to the start of Week 1 – do you feel that the activities are now becoming more straightforward?

Activity 5 Volume

Timing: Allow approximately 5 minutes
  • a.You fill your car with 35.6 litres of fuel one day and four days later, another 15.2 litres. How much fuel in total have you put in your car this week in centilitres? Remember, clicking on ‘reveal comment’ will give you additional hints and tips.


multiline equation line 1 Volume of fuel equals 35.6 litres plus 15.2 litres line 2 equals 50.8 litres

one litre equals 100 cl

Converting from a physically larger to a physically smaller unit, means you need to multiply.

multiline equation line 1 So volume of fuel in cl equals left parenthesis 50.8 multiplication 100 right parenthesis cl line 2 equals 5080 cl

  • b.A bottle contains 14 cl of medicine. The dose is 5 ml. How many doses can be given from this bottle?

    Click on reveal comment if you need a hint.


You are dealing with different units here, so you need to start by converting 14 cl to ml or 5 ml to cl.

You may find it easier to convert 14 cl to ml.


To find the number of doses, the volume of the bottle and the dose need to be in the same units.

There are 10 ml in 1 cl.

Therefore, 14 cl equals left parenthesis 14 multiplication 10 right parenthesis ml equals 140 ml

multiline equation line 1 So comma number of doses in the bottle equals 140 ml division five ml line 2 equals 28

You have probably guessed by now that the next topic will be the imperial units for volume. Some of these will no doubt prove more familiar than others, as they are still used in some everyday situations, such as buying drinks.