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Optimization problem

  1. Jul 1, 2013 #1
    1. The problem statement, all variables and given/known data
    What is a height of a maximum volume cone when slant height is s?

    3. The attempt at a solution

    s^2 = h^2 + r^2

    r^2=s^2-h^2

    V=1/3*pi*r^2*h
    V=pi/3*(s^2-h^2)*h
    V=pi/3*(s^2*h-h^3)
    V'=pi/3*(s^2-3h^2) → s^2-3h^2=0

    s^2=3h^2 → (s^2)/(3)=h^2 → h= s/SQRT(3)

    My textbook says that correct solution is s*sqrt(3)/3 ???

    Edit:
    Solved it, delete thread please.
     
    Last edited: Jul 1, 2013
  2. jcsd
  3. Jul 1, 2013 #2

    Mark44

    Staff: Mentor

    We don't generally delete threads on demand.
     
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