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Minimizing Surface Area/Volume

  1. Nov 17, 2009 #1
    1. The problem statement, all variables and given/known data
    I need to find a solution to make a large capsule ( top and bottom are hemispheres and middle is a cyliner) The capsule must be big enough to hold .25 cubic meters of medicine. One hemisphere's materials costs $.0025 per square centimeter and the other hemisphere and cylinder materials costs $ .0015 per square centimeter. I need to know the optimal measurements to minimize the total materials cost for the case, as well as the total materials cost for this optimal design.


    2. Relevant equations

    V of sphere= 4/3pi r^3
    V of cylinder= pi r^2h
    SA of sphere=4 pi r^2
    SA of cylinder= 2pi r^2+ 2pi rh

    3. The attempt at a solution
     
  2. jcsd
  3. Nov 17, 2009 #2

    tiny-tim

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    Welcome to PF!

    Hi Mldancer125! Welcome to PF! :wink:

    Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
     
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