Estimate and Compare Volumes of Cubes and Cuboids

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. You must convert to the correct unit before doing the calculation. If you try to convert the answer, you will 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.