How to Calculate Sphere Size

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Sphere size is calculated using two measures: the volume (how much space the sphere takes up) and the surface area (the total area of the sphere's surface). Both sphere size and surface area can be easily calculated if you know the radius or diameter of the sphere. The formula for volume is 4/3 times pi times the radius cubed, or 4/3πr^3. The formula for surface is 4 times pi times the radius squared, or 4πr^2.

  • Calculate the radius of the sphere from the information given about the sphere. If you know the diameter (distance through the sphere through the center), divide by two to find the radius. If you know the circumference (distance around the center of the sphere), divide by 2π.

  • Find the cube of the radius by multiplying it by itself twice. For example, the cube of 3 is 3 times 3 for 9, times 3 again equals 27.

  • Multiply the cube of the radius times 4/3π. π is commonly approximated as 3.14, so 4/3π is approximately 4.19. 4.19 times the radius cubed equals the volume of the sphere.

  • Find the square of the radius by multiplying it by itself.

  • Multiply the result in Step 4 by 4π (4π is equal to approximately 12.56). The answer is equal to the surface area of the sphere.

References

  • Photo Credit Yagi Studio/Photodisc/Getty Images
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