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Homework Help: Optimization - Find dimension of a cup that uses least amount of paper

  1. Apr 9, 2009 #1
    1. The problem statement, all variables and given/known data
    A cone-shaped paper drinking cup is to be made to hold 30 cm3 of water. Find the height and radius of the cup that will use the smallest amount of paper.

    2. Relevant equations
    volume of a cone (1/3)(pi)(r^2)(h) = 30
    SA of a cone pi(r)[sqrt(r^2 + h^2)]

    3. The attempt at a solution
    solve volume for h
    plug h into SA
    derive SA
    calculate r
    solve for h

    I'm understanding how to do it, I just can't get the right answers.
  2. jcsd
  3. Apr 9, 2009 #2


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    Homework Helper

    Re: Optimization

    Show your work, so we can know where did you go wrong.
  4. Apr 9, 2009 #3
    Re: Optimization

    h = 90/(pir^2)

    derivative of SA = 2pi*pir^2*r^2+90pi, denominator not needed, setting equal to zero.
  5. Apr 9, 2009 #4
    Re: Optimization

    I got a different derivative (even after clearing out some denominators).
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