1. May 19, 2008 #1

   Amith2006

   

   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

    

   Amith2006, May 19, 2008
2. 
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3. May 19, 2008 #2

   lzkelley

   

   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.

    

   lzkelley, May 19, 2008
4. May 21, 2008 #3

   Amith2006

   

   thanx buddy.

    

   Amith2006, May 21, 2008
5. May 21, 2008 #4

   HallsofIvy

   

   Staff Emeritus

   Science Advisor

   The complete answer involves "Calculus of Variations".

    

   HallsofIvy, May 21, 2008

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