Question

A cone with a radius of 12 cm and a height of 12 cm has the same volume as a cylinder with a radius of 8 cm. What is the height of the cylinder?

Answer 1

First, substitute the given radius and given height of the cone into the formula for the volume of a cone. 

Volume of a cone:  (1/3) pi r^2 h
In this case, the cone volume is (1/3) pi (12 cm)^2 (12 cm) = 576 cm^3

Vol. of a rt. cylinder:  pi r^2 h
In this case, the vol. of the rt. cyl. is pi (8 cm)^2 h.

The two different shapes have the same volume.  Therefore, set the two formulas (above) equal to each other:

576 pi cm^3 = pi (8cm)^2 h.  This becomes

576 pi cm^3 = pi (64 cm^2) h.  "pi" cancels out, leaving us with

576 cm^3
------------- = h.       This is the height of the cylinder, in cm.
 64 cm^2