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Applied Optimization Problem

  1. Nov 16, 2011 #1
    1. The problem statement, all variables and given/known data
    Find the volume of the largest right circular cone that can be inscribed in a sphere of radius 3.


    2. Relevant equations
    V=π*r^2*h/3
    A=πr^2 + πrl

    3. The attempt at a solution
    I did multiple things that I'm not sure are correct. I took the derivative for the volume with the value of h set to (9-x^2)^(1/2). The derivative I got was;
    3π/2 * (9-x^2)^(-1/2) * (-2x)

    Not really sure what to do. Think I need a hint on the steps that need to be taken. Picture of problem attached.
     

    Attached Files:

    Last edited: Nov 16, 2011
  2. jcsd
  3. Nov 16, 2011 #2

    eumyang

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    In your diagram, I would replace "y" with "h - 3". Next, find x in terms of h. Then substitute into the volume of a right circular cone
    [itex]V = \frac{1}{3}\pi r^2 h[/itex]
    (with r = x here) and you'll have a function with one variable, h. Now find dV/dh and go on from there.
     
  4. Nov 16, 2011 #3

    Ray Vickson

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    Write out your expression for V in terms of x. I got a different derivative dV/dx than yours.

    RGV
     
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