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.
While you are here..
... I have a small favor to ask. Over the years we have used advertising to support the site so it can remain free for everyone.
However, advertising revenue is falling and I have always hated the ads. So, would you go to Patreon and become a patron of the site?
When we reach the goal I will remove all advertising from the site.
It only takes a minute and any amount would be greatly appreciated.
Thank you for considering it! – John Page
Become a patron of the site at patreon.com/mathopenref
Related topics
(C) 2011 Copyright Math Open Reference. All rights reserved
