Volume of a sphere

Definition: The number of cubic units that will exactly fill a sphere.
Try this Drag the orange dot to adjust the radius of the sphere and note how the volume changes.

The volume enclosed by a sphere is given by the formula 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 volume. Since the 4, 3 and pi are constants, this simplifies to approximately

This formula was discovered over two thousand years ago by the Greek philosopher Archimedes. He also realized that the volume of a sphere is exactly two thirds the volume of its circumscribed cylinder, which is the smallest cylinder that can contain the sphere.

If you know the volume

By rearranging the above formula you can find the radius: where v is the volume

Note Most calculators don't have a cube root button. Instead, use the calculator's "raise to a power" button and raise the inner part to the power one third.

Interesting fact

For a given surface area, the sphere is the one solid that has the greatest volume. This why it appears in nature so much, such as water drops, bubbles and planets.

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.
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