Finding the Volume of a Sphere
(KS3, Year 8)

The Lesson

The volume of a sphere is found using the formula:

In this formula, r is the radius of the sphere. The image below shows what we mean by radius:

"Find the Volume" Widget

Here is a widget to help you learn the formulas to find the volumes of different shapes.

How to Find the Volume of a Sphere

Question

What is the volume of a sphere with a radius of 5 cm, as shown below?

Step-by-Step:

1

Start with the formula:
Volume = 4πr3 ⁄ 3
Don't forget: π is pi (≈ 3.14) and r3 = r × r × r (r cubed) and ⁄ means ÷.

2

Substitute the radius into the formula. In our example, r = 5.
Volume = 4 × π × 53 ⁄ 3 Volume = 4 × π × 125 ÷ 3 Volume = 4 × 3.14 × 125 ÷ 3 Volume = 523.3 cm3

Answer:

The volume of the sphere with a radius of 5 cm is 523.3 cm3.

Lesson Slides

The slider below shows another real example of how to find the volume of a sphere. Open the slider in a new tab

What Is a Sphere?

A sphere is a ball-shaped object. Each point on its surface is the same distance away from the center.

The Main Parts of a Sphere

The radius is the distance from the center of a sphere to its surface. The diameter is the line that goes through the center of the sphere and joins two opposite points on the surface. It is twice the length of the radius.

Who Discovered How To Find the Volume of a Sphere?

Archimedes discovered was the first to prove the volume of a sphere.

A Sphere in a Cylinder

If a sphere is placed in a cylinder, the volume of the sphere is exactly two-thirds the volume of the cylinder. Can you work out why?
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See Also

What is the radius?