What is the surface of a sphere which has a radius of 6cm? (How to calculate surface area of a ball)


The surface area of a sphere can be found using the following formula:

S = πd²

S stands for the surface area, π is Pi (a number equal to 3.142) and d is the diameter of the sphere. So if you are asked to work out the surface area of the sphere first make sure you have the diameter of the sphere, then square this diameter and multiply your answer by Pi.

Alternatively you can use the formula S = 4πr², but in the examples that follow we will use S = πd² to calculate the surface area of the spere.

Example 1

The picture shows a solid sphere. The radius of the sphere is 6 cm. Calculate the surface area of the surface. Give the answer to the nearest hundredth.

First you will need to have the diameter of the sphere. The diameter of the sphere will be double the length of the radius:

6 × 2 = 12 cm.

So the diameter of this sphere is 12 cm.

You can no plug this value into the formula for the surface area of a sphere:

S = πd²

S = π × 12² (make sure that you square the diameter before multiplying by Pi)

S = π × 144

S = 452.39 cm² (rounded to the nearest hundredth)

So the surface area of this sphere is 452.39 squared centimetres.

Example 2

A spherical shaped ball has a diameter of 11 inches. Work out the surface area of the ball. Give your answer to the nearest whole number.

This time the question already gives the diameter of the sphere. So you can plug d = 11 directly into the formula for the surface area of a sphere:

S = πd²

S = π × 11² (make sure that you square the diameter before multiplying by Pi)

S = π × 121

S = 380 inches² rounded to the nearest whole number.

So the surface area of this sphere is 380 square inches.

Example 3

A sphere of radius 3m is to be painted red. A tin of red paint covers 20m². Work out the amount of tins of paint needed to cover the sphere.

To find out the amount of tins of paint you need you will have to find the surface area of the sphere. This is because you are painting around the outside of the sphere. Like example 1, you are given the radius of the sphere, so this has to be double to give you the diameter of the sphere:

3 × 2 = 6 m.

So the diameter of this sphere is 6 m.

You can no plug this value into the formula for the surface area of a sphere:

S = πd²

S = π × 6² (make sure that you square the diameter before multiplying by Pi)

S = π × 36

S = 113 m² (rounded to the nearest whole)

So the surface area of this sphere is 113 squared metres.

All you need to do next is divide 113 by 20:

113 ÷ 20 = 5.65

So you will need to buy 6 tins of red paint (round 5.65 upwards as you can't buy a fraction of a tin!)

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