There are formulae to work out the volumes of these shapes:
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
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?
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.
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.
Want to understand this further and learn how this links to other topics in maths?
Why not watch this video?