Skip to content
Skip to main content

About this free course

Download this course

Share this free course


Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

3.3 Volumes

What is a volume? The word usually refers to the amount of three-dimensional space that an object occupies. It is commonly measured in cubic centimetres (cm3) or cubic metres (m3).

A closely related idea is capacity; this is used to specify the volume of liquid or gas that a container can actually hold. You might refer to the volume of a brick and the capacity of a jug – but not vice versa. Note that a container with a particular volume will not necessarily have the same amount of capacity. For example, a toilet cistern will have a smaller capacity than its total volume because the overflow pipe makes the volume above the pipe outlet unusable. Some units are used only for capacity – examples are litre, gallon and pint; cubic centimetres and cubic metres can be used for either capacity or volume.

One of the simplest solid shapes is a cube; it has six identical square faces.

Volume of a cube = length × length × length = (length) 3

A cuboid (or rectangular box) has 6 rectangular faces as shown below.

Volume of a rectangular box = length × breadth × height

The length × breadth is the area of the bottom (or top) of the box, so an alternative formula is

volume of box = area of base × height.

The volume formula can also be written as

volume  = area of end face × length


volume = area of front face × breadth