You should be familiar with the concept of **scale factor** and calculating lengths of **similar** shapes.

Here, we will look at questions involving **volume scale factor **.

__Example__

These two cubes are similar.

Smaller cube length = 4 cm

Volume of the smaller cube = 64 cm³

Larger cube length = 8 cm

What is the volume of the larger cube?

__Method__

1. Find the **scale factor of length** by dividing corresponding lengths. 8 ÷ 4 = 2

2. **Cube the scale factor** 2 x 2 x 2 = 8

3. **Multiply** by the volume if you are finding the larger shape, **or divide** if you want the smaller shape. (In this case, we want the larger shape, so we multiply) 64 x 8 = 512 cm³

The step that students tend to forget is Step 2. You ** must** be able to recall that a scale factor of length needs to be

**in order to make a comparison of two shapes' volumes.**

__cubed__

__Example 2__

Large cuboid length = 18 cm

Volume of large cuboid = 1620 cm³

Small cuboid length = 6 cm

What is the volume of the small cuboid?

__Method__

1. Find the **scale factor of length** by dividing corresponding lengths. 18 ÷ 6 = 3

2. **Cube the scale factor** 3 x 3 x 3 = 27

3. **Multiply** by the volume if you are finding the larger shape, **or divide** if you want the smaller shape. (In this case, we want the smaller shape, so we divide) 1620 ÷ 27 = 60 cm³

Knowing cube numbers comes in very useful in these types of question. Just remember the steps in the method and you will be able to find unknown volumes of similar shapes.