Solid Mensuration
posted by Paul .
Two similar cones have volumes 81pi/2 in^3 and 12pi in^3 and slant height of the bigger cone is 7.5 in. Find the integer solution to the height of the similar cone.

bigV/smallV = 81/2 / 12 = 81/24 = (3/2)^3
volumes are in the ratio x^3:1 if the sides are in ratio x:1
so,
bigH/smallH = 3/2
so, 7.5/smallH = 1.5, and smallH = 5