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. 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 mm ^{3}**.

*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.