Lectures on Physics has been derived from Benjamin Crowell's Light and Matter series of free introductory textbooks on physics. See the editorial for more information....

Scaling of the volume of a sphere

n / The big sphere has 125 times more volume than the little one.

In figure n, the larger sphere has a radius that is five times greater. How many times greater is its volume?

Correct solution #1: Volume scales like the third power of the linear size, so the larger sphere has a volume that is 125 times greater (53 = 125).

Correct solution #2: The volume of a sphere is V = (4/3)πr3, so

Incorrect solution: The volume of a sphere is V = pr3, so

(The solution is incorrect because (5r1)3 is not the same as 5r3 1.)

Last Update: 2010-11-11