Dimensions of cone with smallest volume that can hold a cylinder

[chung963]

Homework Statement

A cylinder of height 45mm and radius 12mm is placed inside a circular cone.
What are the dimensions of the cone with the smallest volume to enclose this cylinder

Homework Equations

v=1/3(pi)r^2h
v=(pi)r^2h
SA=2(pi)rh

The Attempt at a Solution

I substuted values into the cylinder equation and got 20,357mm^2 volume of cylinder and made an equation in terms of h and substitued into the cone formula but answer didnt work out.
Final answer is r=18 and h=135

 

[vela]

Please post your detailed calculations. Generic descriptions of what you tried aren't very helpful.