Optimization and L'Hospital's rule

1)

Deriving the right side gives me:

Since the top goes towards a positive number (infinity) and the bottom goes to 0,

Is my logic wrong?

2) A cone-shaped paper drinking cup is to be made to hold 33 cm^3 of water. Find the height and radius of the cup that will use the smallest amount of paper. (Give your answers correct to two decimal places.)

where

So

Am I starting this off the right way? Because if I am, this looks disgusting. I was trying to derive the Surface Area formula just in terms of r, and then finding the minimum I could plug it back into the volume formula to gind the minimum h?

Am I wrong in my approach?