The formula for the volume of a sphere, V, in terms of its radius, r, is:

V = 4/3 πr^{3}

We can rearrange this formula to make **r** the subject.

If we multiply both sides by 3, we reach:

3V = 4πr^{3}

Then we can divide both sides by 4π to reach:

r^{3} = 3V / 4π

Finally, we need to find the cubed root of both sides and the formula for the radius of a sphere, **r**, in terms of its volume, **V**, is:

**Example**

Calculate the radius, r cm, of a sphere which has a volume of 100 cm^{3}.

Give your answer to 3 significant figures.

V = 4/3 πr^{3}

100 = 4/3 πr^{3}

Multiply both sides by 3: 300 = 4πr^{3}

Divide both sides by 4π: 300 / 4π = r^{3}

Find the cube root of this total: r = ^{3}√ 300 / 4π

r = ^{3}√23.873... = 2.8794... ≈** 2.88** cm (to 3 s.f.)

It looks complicated, but just take it one step at a time.

Let's give it a go!