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.
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Area of a Sphere Calculators
We have two separate calculators for the area of a sphere.
Our first calculator will take a measurement for the radius or diameter of the sphere and find the surface area.
Our second calculator will take a surface area and find the radius and diameter of the sphere.
Area of a Sphere Calculator 1
This calculator finds the surface area of a sphere when the radius or diameter is known.
How the Calculator Works
- Select if you want to use the radius or diameter (default is radius).
- For the value, you can choose a whole number, decimal or fraction.
- You can type a fraction by typing the numerator then '/' then the denominator.
- You can type a mixed number by typing the whole-number part, then a space then the fraction part.
- Examples: 2 1/2 (two and one-half); 3 4/5 (three and four-fifths); 7 1/3 (seven and one-third).
- Choose your units of measurement (default is cm)
- Choose your desired accuracy (default is 2 decimal places)
- Click the Find Area button
- You will be given two answers for the area, one in terms of Pi (π) and the other answer as a decimal value.
Area of a Sphere Calculator 2
This calculator finds the radius and diameter of the sphere when the surface area is known.
How the Calculator Works
- Choose the surface area value: you can choose a whole number, decimal or fraction.
- Choose your units of measurement (default is none)
- Choose your desired accuracy (default is 2 decimal places)
- Click the Find Radius button
- You will be shown the radius and diameter of the sphere as a decimal to the required accuracy.
Surface Area of a Sphere Formula
The formula for the area of a sphere is: A = 4 πr2, where A is the area, and r is the radius of the circle.
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: \[ diameter = 6.308 \times 2 = 12.6 \; cm \; to \; 1 \; decimal \; place. \]
Surface Area of a Sphere Worksheets
We have created two worksheets to help you practice this skill.
The first sheet involves working out the surface area of a range of spheres where the radius is given.
The second sheet involves working out the surface area of spheres where the radius or diameter are given.
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Each calculator page comes with worked examples, formulas and practice worksheets.
More Area Support and Resources
We have a range of other area worksheets and support pages for a range of different 2d shapes.
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