I worked through this problem; what did I do wrong? Thanks so much:

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.

30 = 1/3*pi*r^2*h

90/(pi*r^2) = h

SA of a cone = pi*r *(sqrt(r^2 + h^2))

SA(r) = pi*r * (sqrt(r^2 + (90/(pi*r^2))^2)

pi*r^2 * (r^2 + (8100/(pi*r^4))

pi*r^4 + (8100/r^2)

SA'(r) = 4*pi*r^3 - 8100/r^3

4*pi*r^6 = 8100/r^3

r^6 = (8100/4*pi)

r = 2.939