Optimization Problem with Cylinder

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Homework Statement

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?

Homework Equations

V=$$\pi$$r²h

The Attempt at a Solution

So I first tried solving for r in termsof h, but from there I am not sure how I am suppose to do this problem. Could someone please help me?

 

[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?