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 cm ^{3} 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 cm ^{3}**.

So **480 **cubes will fit.

**e.g. Calculate the volume of this cube in mm ^{3}.**

**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 mm^{3} 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 mm ^{3}**.

*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?