MathDB

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

C

and a frustum-shaped solid

F

, in such a way that the ratio between the areas of the painted surfaces of

C

and

F

and the ratio between the volumes of

C

and

F

are both equal to

k

. Given that

k=m/n

, where

m

and

n

are relatively prime positive integers, find

m+n

Problem Statement