2004 AIME I Problems/Problem 11
Problem
A solid in the shape of a right circular cone is 4 inches tall and its base has a 3-inch radius. The entire surface of the cone, including its base, is painted. A plane parallel to the base of the cone divides the cone into two solids, a smaller cone-shaped solid 
and a frustum-shaped solid 
in such a way that the ratio between the areas of the painted surfaces of and 
and the ratio between the volumes of and are both equal to 
Given that 
where 
and 
are relatively prime positive integers, find 
