A simple guide to working out the volume of a spere or ball V = (4/3)*Pi*r^3

Updated on August 27, 2012

The volume of a sphere (a ball) can be calculated using the following formula:

V= (4/3) πr³

All you need to know is the radius of the sphere. If you are given the diameter make sure you half this to give the radius of the sphere.

If you don’t like algebra follow this result:

Example 1

A sphere has a radius of 8cm. Work out the volume of the sphere.

Since the radius of the sphere is 8 substitute r = 8 into the formula for the volume of a sphere:

V = (4/3) × π × 8³

Just type this into your scientific calculator:

= 2145 cm³ to the nearest whole number.

Example 2

A spherical ball has a radius of 5cm. Work out the volume of the ball.

To do this you just need to use the formula for calculating the volume of a sphere.

Since the radius of the sphere is 5 substitute r = 5 into the formula for the volume of a sphere:

V = (4/3) × π × 5³

Just type this into your scientific calculator:

= 524 cm³ to the nearest whole number.

Example 3

Another sphere has a diameter of 14m. Work out the volume of the sphere.

This time you are given the diameter of the sphere so this will have to be halved before you can work out the volume of the sphere:

14 ÷ 2 = 7m

So the radius of the sphere is 7m.

Since the radius of the sphere is 7 substitute r = 7 into the formula for the volume of a sphere:

V = (4/3) × π × 7³

Just type this into your scientific calculator:

= 1438 cm³ to the nearest whole number.

Example 4

A sphere has a radius of 35 inches. Work out the volume of the sphere.

Since the radius of the sphere is 35 substitute r = 35 into the formula for the volume of a sphere:

V = (4/3) × π × 35³

Just type this into your scientific calculator:

= 180,000 cubic inches

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