Cubes and Cuboids: Estimate and Compare Volumes

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

Cube

We must 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 × side length × side length

Cuboid

You must know: the length; the width; and the height

Volume of cuboid = length × width × height

e.g. 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.

e.g. 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.

Volume of cube = side length × side length × side length = 70 × 70 × 70 = 49 × 7 × 10 × 10 × 10 = 343 × 1000 = 343000 mm³.

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