why do you have to divide by 3 when finding the volume of a cone?

This is due to the fact that the volume of a pyramidal object is always 1/3 that of its associated prismatic object (an object on the same base with the same height). So, the volume of a cone is 1/3 of that of its associated cylinder.

Here's the proof from Euclid's Elements......http://aleph0.clarku.edu/~djoyce/java/elements/bookXII/propXII10.html

Warning......it's a little  difficult !!!!