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 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.

**Example 2**

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. 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 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.