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Optimization Problems

  1. Mar 31, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the dimensions of the right circular cone of maximum volume that can be inscribed in a sphere of radius 15cm.


    2. Relevant equations



    3. The attempt at a solution

    let r be radius of circular base of cone
    let y be height of small right triangle
    let h be height of cone



    r^2 + y^2=225
    y=sqrt(225-r^2)

    h=15+y

    V=(1/3)pir^2(sqrt(225-r^2) + 15)

    Now to find V'...I get to 9r^4-2670r^2+195750 = 0
    0=3(3r^4-890r^2+65250)

    Need to solve for r.

    Took about 2323 lines.

    Final dimensions; r=11.5 roughly

    h=24.63

    maax volume is 3411.05 ?
     
    Last edited: Mar 31, 2009
  2. jcsd
  3. Mar 31, 2009 #2
    Can somebody confirm this? Thank you :)
     
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