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Measures : Key Stage 4 : Mathematics Content Knowledge


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Key Stage 4
Measures
Question 2 of 12

1. How confident are you that you understand

b. the distinction between volume and capacity?


Example

The volume of an object is the amount of three-dimensional space that it occupies. The capacity of a container is the amount of three-dimensional space inside it, or the maximum amount of liquid volume that it will hold.

Colloquially, volume is often used instead of capacity. For example, we may say a mug has a volume of half-a-pint, meaning its capacity (rather than the volume of clay used to make it).

Liquid volume or capacity and solid volume are conventionally measured in different units, although the concepts are the same. Liquid volume is measured in litres and millilitres (or pints), and solid volume is measured in cubic centimetres, cubic metres, and so on.

In the metric system, units for liquid and solid volume are related in a simple way: 1 ml is the same volume as 1 cm3, and 1 litre is the same volume as 1000 cm3.

What this might look like in the classroom

Question 1:
Suggest suitable units for measuring:
  1. The volume of a computer mouse
  2. The volume of water in a swimming pool
  3. The amount of drink in a can
  4. The volume of the rubber on the end of a pencil
  5. The volume of rock removed from a quarry in one day
  6. The amount of water a swimming pool can hold

Answer 1:
  1. Cubic centimetres
  2. Cubic metres
  3. Millilitres
  4. Cubic millimetres
  5. Cubic metres
  6. Litres

Taking this mathematics further

Research the history of the metric system:
  • When was it developed?
  • Who developed it?
  • Why did they develop it?
  • What is a metre?
  • Where is the metre?

In addition to the standard prefixes of milli, centi and kilo, find out what these prefixes mean in the metric system:
  • Deci
  • Deca
  • Hecto

Making connections

The metric system also interrelates volume and capacity with mass:
  • 1 millilitre of water has a mass of 1 gram
  • 1 litre of water has a mass of 1 kilogram
  • 1 cubic metre of water has a mass of 1 tonne.

As such, in the metric system, length, area, volume, capacity and mass are all related.

Using the connection between volume and capacity means that irregular shaped objects can have their volume measured by considering the amount of water that they displace

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