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.