# Optimixation, Calculus 1

1. Dec 9, 2008

### Reedeegi

1. The problem statement, all variables and given/known data
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.

2. Relevant equations
S = $$\pi$$ r2 $$\sqrt{r2+h2}$$

3. The attempt at a solution
I'm having trouble getting off my feet... any suggestions?

2. Dec 9, 2008

### 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.