Estimate and Compare Volumes of Cubes and Cuboids

There are formulae to work out the volumes of these shapes:

Cube

We need to know the side length.

Remember that the length, the width and the height will all be equal to the side length because this is a cube.

Volume of cube = side length x side length x side length

Cuboid

We need to know the length, the width and the height.

Volume of cuboid = length x width x height

Example

How many 1 cm³ cubes will fit into this cuboid?

Answer

The length is 15 cm, the width is 4 cm and the height is 8 cm.

Volume of cuboid  = length × width × height = 15 × 4 × 8 = 60 × 8 = 480 cm³

So 480 cubes will fit.

Example 2

Calculate the volume of this cube in mm³

Answer

The side length is 7 cm, so the width and the height are also 7 cm.

This will be 70 mm

NB: We want the answer in mm³ which is why we should work in mm not cm. It is best to convert to the correct unit before doing the calculation. If you try to convert the answer, you might well get it wrong!

Volume of cube = side length × side length × side length = 70 × 70 × 70 = 49 × 7 × 10 × 10 × 10 = 343 × 1,000 = 343,000 mm³

NB: The length, the width and the height are all interchangeable with each other, depending on how we look at a cuboid.

Let's try some questions now.