Optimization - Find dimension of a cup that uses least amount of paper

[disque]

Homework Statement

A cone-shaped paper drinking cup is to be made to hold 30 cm3 of water. Find the height and radius of the cup that will use the smallest amount of paper.

Homework Equations

volume of a cone (1/3)(pi)(r^2)(h) = 30
SA of a cone pi(r)[sqrt(r^2 + h^2)]

The Attempt at a Solution

solve volume for h
plug h into SA
derive SA
calculate r
solve for h

I'm understanding how to do it, I just can't get the right answers.

 

[Pyrrhus]

Show your work, so we can know where did you go wrong.

 

[disque]

h = 90/(pir^2)

derivative of SA = 2pi*pir^2*r^2+90pi, denominator not needed, setting equal to zero.

 

[Billy Bob]

I got a different derivative (even after clearing out some denominators).