Loading please wait

The smart way to improve grades

Comprehensive & curriculum aligned

Try an activity or get started for free

Radius of Spheres

In this worksheet, children must work out the radius of spheres given their volumes.

'Radius of Spheres' worksheet

Key stage:  KS 3

Curriculum topic:   Geometry and Measures

Curriculum subtopic:   Use 3D Shape Knowledge to Solve Problems

Difficulty level:  

Worksheet Overview

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

V = 4/3 πr3


We can rearrange this formula to make r the subject.


If we multiply both sides by 3, we reach: 

3V = 4πr3


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

r3 = 3V / 4π


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


e.g. Calculate the radius, r cm, of a sphere which has a volume of 100 cm3. Give your answer to 3 significant figures.


V = 4/3 πr3

100 = 4/3 πr3

Multiply both sides by 3: 300 = 4πr3

Divide both sides by 4π: 300 / 4π = r3

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

r = 3√23.873... = 2.8794... ≈ 2.88 cm (to 3 s.f.)

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started

Try an activity or get started for free