Identify Formulae for Lengths, Areas and Volumes

By analysing the dimensions to the right of the equals sign, we can say whether a formula could be for length, area or volume.

A formula for length can only be one-dimensional. 

This means that lengths occur on their own e.g. C = 3d or P = a + 2b

A formula for area can only be two-dimensional. 

This means that lengths occur in pairs e.g. A = 3ab or A = a² + 2ab

A formula for volume can only be three-dimensional. 

This means that lengths occur in threes e.g. C = 5d³ or P = abc + 2a²b

Let's have a go at some questions.