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Find the Radius of a Sphere

In this worksheet, students will work out the radius of spheres given their volumes.

'Find the Radius of a Sphere' worksheet

Key stage:  KS 3

Year:  Year 9 Maths worksheets

Curriculum topic:   Geometry and Measures

Curriculum subtopic:   Use 3D Shape Knowledge to Solve Problems

Popular topics:   Geometry worksheets

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


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:




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.)


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


Let's give it a go!

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