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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:

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.

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

• 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.

### Comment

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.