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Figure of largest area

  1. May 19, 2008 #1
    1. The problem statement, all variables and given/known data
    For a two DIMENSIONAL figure of given perimeter why does the circle have the largest area? Similarly, of all three dimensional figures of given volume the sphere has the largest area. why?

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 19, 2008 #2
    You can set up a differential equation describing the relationship between area and perimeter for varying shapes... solving for the maximum results in the equation for a circle. The same thing in 3D results in a sphere.
     
  4. May 21, 2008 #3
    thanx buddy.
     
  5. May 21, 2008 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    The complete answer involves "Calculus of Variations".
     
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