Surface area of a sphere

Definition: The number of square units that will exactly cover the surface of a sphere.
Try this Drag the orange dot to adjust the radius of the sphere and note how the area changes.


The surface area of a sphere is given by the formula Formula for area of a sphere Where r is the radius of the sphere. In the figure above, drag the orange dot to change the radius of the sphere and note how the formula is used to calculate the surface area.

This formula was discovered over two thousand years ago by the Greek philosopher Archemedes. He also realized that the surface area of a sphere is exactly equal to the area of the curved wall of its circumscribed cylinder, which is the smallest cylinder that can contain the sphere. See Surface area of a cylinder.

If you know the surface area

By rearranging the above formula you can find the radius: Formula for radius of a sphere given the area where a is the surface area.

Interesting facts

  1. For a given volume, the sphere is the shape that has the smallest surface area. This why it appears in nature so much, such as water drops, bubbles and planets.
  2. The surface area of a sphere is exactly four times the area of a circle with the same radius. You can see this in the area formula, since the area of a circle is and the surface area of a sphere is

Things to try

    • In the figure above, click "hide details".
    • Drag the orange dot to resize the sphere.
    • Calculate the volume of the sphere
    • Click "show details" to check your answer.
    • In the figure above, click "reset" then uncheck "show radius"
    • Drag the orange dot to resize the sphere.
    • Calculate the radius of the sphere from the volume
    • Click "show radius" to check your answer.

Related topics

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