Spheres. How to find the volume of a sphere?

To find the volume of a sphere all you need to do is use the following formula:

V = 4/3πr³

That is Volume = 4/3 × Pi × r³

Pi is a mathematical constant equal to 3.14 (2 decimal places), but you can use your Pi button on your calculator.

Let’s take a look at some examples:

Example 1

Find the volume of a sphere of radius 8cm.

Since we have the radius of the sphere all we need to do is substitute this into our formula for the volume of a sphere.

V = 4/3πr³

V= 4/3 × π × 8³

V = 2681cm³ to the nearest whole number.

Example 2

Another sphere has a diameter of 24cm. What is the volume of the sphere?

This time the question gives us the diameter of the sphere so we need to halve this answer to give the radius.

So the radius of the sphere is 12. Now all we need to do now is substitute this radius into the formula.

V = 4/3πr³

V= 4/3 × π × 12³

V = 7238 cm³ to the nearest whole number.

Example 3

A marble (shaped as a sphere) has a diameter of 1cm. What is the volume of the marble?

Again, the question gives us the diameter of the sphere so we need to halve this answer to give the radius.

So the radius of the sphere is 0.5cm. Now all we need to do now is substitute this radius into the formula.

V = 4/3πr³

V= 4/3 × π × 0.5³

V = 0.52 cm³ to 2 decimal places.

So our marble has a volume of 0.52 centimetres cubed.

Summary

To find the volume of a sphere use the formula V = 4/3πr³. Make sure you substitute the radius into the formula and not the diameter.