Thread: Cylinder Optimization

A cylindrical can hold 460 cubic centimeters of soup.
Find the dimensions of the soup can that uses the least amount of material.

I know that v=pi*(r^2)h and I have to optimize that by taking the derivative and setting equal to zero, but I'm not sure how to get h in terms of r. I had h=460/pi(r^2), but when I solved the problem it didn't turn out right. Maybe I'm doing something wrong?

We have

Surface area is:

Solve the volume equation for r or h, whatever.

Then, sub into S. It will then be in terms of one variable. Differentiate, set to 0 and solve away.