Optimizing Cone-Shaped Drinking Cup Design

[Reedeegi]

Homework Statement

A cone-shaped paper drinking cup is to be made to hole 27 cm³ of water. Find the height and radius of the cup that will use the smallest amount of paper.

Homework Equations

S = \pi r² \sqrt{r²+h²}

The Attempt at a Solution

I'm having trouble getting off my feet... any suggestions?

 

[Dick]

The surface area of a cone is S=pi*r*sqrt(r^2+h^2). No r^2 in front of the square root. What's the formula for the volume V? V=27cm^3. Solve the volume formula for r or h and substitute into the surface formula. So you have S as a function of one variable. Now minimize it. BTW I think in English, "getting off your feet" means something closer to lying down and taking a nap. Don't do that. Just try and solve it.