Succeed with maths – Part 2
◄Previous: 2.3 Relating SI and imperial: mass

# 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

Allow approximately 5 minutes

1. 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.

## Answer

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

2. 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.

## Discussion

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.

## Answer

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,

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.

◄Contents►Next: 3.1 Volume: the imperial units

OpenLearn - Succeed with maths – Part 2
Except for third party materials and otherwise, this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 Licence, full copyright detail can be found in the acknowledgements section. Please see full copyright statement for details.