Calculate the Volume of Cubes and Cuboids

Use the following 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

 

We must know the length, the width and the height.

 

Volume of cuboid = length × width × height

 

 

 

e.g. Calculate the volume of this cuboid in cm³.

 

 

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

 

 

 

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 you look at a cuboid.

 

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