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Optimization Problem with Cylinder

  1. Feb 14, 2009 #1
    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[tex]\pi[/tex] 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


    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. jcsd
  3. Feb 15, 2009 #2


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    Gold Member

    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 [tex]V=16 \pi[/tex], 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?
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