Calculate Sides and Volumes of Similar Shapes Using Volume Scale Factors

In this activity, we are going to be looking at the volume scale factor of similar shapes. 

A similar shape has the same size angles, but the sides are proportionally bigger or smaller.

We use scale factor to help us to work out any missing lengths.

Area scale factor - this is where we square the scale factor.

For volume scale factor - we cube the scale factor! 

This might seem obvious since:

length is measured in cm
area in cm²
volume in cm³

If scale factor = 2

Area scale factor is 2² = 2 x 2 = 4

Volume scale factor = 2³ = 2 x 2 x 2 = 8

Let's look at a question to help us to understand this.

Example

Two similar shapes have a scale factor of 3

What is the volume scale factor?

Answer

As we said above, we can cube the scale factor to get the volume scale factor!

Volume scale factor = 3³ = 3 x 3 x 3 = 27

You can see from the diagram above that the volume of the bigger shape is 27 if the scale factor is 3.

Are you ready to have a go at some questions?