Optimization Problem with Cylinder

1. Feb 14, 2009

toasted

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

The volume of a cylindrical tin can with a top and a bottom is to be 16$$\pi$$ cubic inches. If a minimum amount of tin is to be used to construct the can, what must be the height, in inches, of the can?

2. Relevant equations

V=$$\pi$$r2h

3. The attempt at a solution
So I first tried solving for r in termsof h, but from there Im not sure how Im suppose to do this problem. Could someone please help me?

2. Feb 15, 2009

danago

You are trying to minimize the surface area of the can. What is the surface area of a cylinder of radius r and height h?

You are told that no matter what h and r are, you must always have $$V=16 \pi$$, hence the radius r is dependent on what the height h is. For a given h, what should the radius of the can be?

You should then be able to come up with an expression for the surface area of the can as a function of height only. How can you find the minimum value of a function?