# Area of a Sphere Calculator

Welcome to our Area of a Sphere Calculator page.

We explain how to find the surface area of a sphere and provide a quick calculator to work it out for you, step-by-step.

There is also a separate calculator which will find the radius and diameter of a sphere, if you already know the surface area.

### Area of a Sphere Calculator 1

Area of a Sphere Calculator ### Area of a Sphere Calculator 2

Area of a Sphere Calculator 2

### Surface Area of a Sphere Examples

#### Area of a Sphere Example 1

Find the surface area of the sphere below to 1 decimal place. The formula for the area of a sphere is: $A = 4 \pi r^2$

If we substitute the values of the radius into this equation, we get: $A = 4 \pi (8)^2 = 4 \pi (64) = 256 \pi$

This gives us a final answer of: $A = 804.2 \;\ cm^2$

#### Area of a Sphere Example 2

A large inflatable ball has a radius of 1 ½ meters. What is the surface area of the ball? Give your answer to 2 decimal places. The formula for the area of a sphere is: $A = 4 \pi r^2$

If we substitute the values of the radius into this equation, we get: $A = 4 \pi (1 {1 \over 2})^2 = 4 \pi ({9 \over 4}) = 9 \pi$

This gives us a final answer of: $A = 28.27 \;\ m^2$

#### Area of a Sphere Example 3

A basketball has a diameter of 9.55 inches. What is the surface area of the ball? Give your answer to 1 decimal place. The first step is to find the radius of the ball.

The diameter of the ball is 9.55 inches. To find the radius, we have to halve the diameter (or divide the diameter by 2).

$9.55 \div 2 = 4.775 \; inches$

The formula for the area of a sphere is: $A = 4 \pi r^2$

If we substitute the values of the radius into this equation, we get: $A = 4 \pi (4.775)^2 = 4 \pi (22.800625) = 91.2025 \pi$

This gives us a final answer of: $A = 286.5 \;\ in^2$

#### Area of a Sphere Example 4

A ball has a surface area of 500 square cm. What is the diameter of the ball? Give your answer to 1 decimal place. In this case, we know the surface area of the ball, but we need to find the diameter.

The formula for the area of a sphere is: $A = 4 \pi r^2$

This means that: $r^2 = {A \over 4 \pi}$

This means that the radius $r = \sqrt ({A \over 4 \pi}) \; or \; {1 \over 2} \sqrt {A \over \pi}$

If we substitute the values of the surface area into this equation, we get: $r = {1 \over 2} \sqrt (500 \over \pi)$

This means that: $r = {1 \over 2} \sqrt (159.155)$

So $r = {1 \over 2} (12.616) = 6.308 cm$

The diameter is equal to twice the radius.

This gives us a final answer of: $diameter = 6.308 \times 2 = 12.6 \; cm \; to \; 1 \; decimal \; place.$

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