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Math Help - Optimization Problem

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    32

    Optimization Problem

    I worked through this problem; what did I do wrong? Thanks so much:

    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.

    30 = 1/3*pi*r^2*h

    90/(pi*r^2) = h

    SA of a cone = pi*r *(sqrt(r^2 + h^2))



    SA(r) = pi*r * (sqrt(r^2 + (90/(pi*r^2))^2)

    pi*r^2 * (r^2 + (8100/(pi*r^4))

    pi*r^4 + (8100/r^2)



    SA'(r) = 4*pi*r^3 - 8100/r^3

    4*pi*r^6 = 8100/r^3

    r^6 = (8100/4*pi)

    r = 2.939
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  2. #2
    Newbie
    Joined
    Oct 2009
    Posts
    11
    > simplify(pi*r^2 * (r^2 + (8100/(pi*r^4))));

    > diff(1/r^2*(r^6*pi+8100),r);

    > solve(-2/r^3*(r^6*pi+8100)+6*r^3*pi,r);

    4050^(1/6)/pi^(1/6),
    (1/2+1/2*I*3^(1/2))*4050^(1/6)/pi^(1/6),
    (-1/2+1/2*I*3^(1/2))*4050^(1/6)/pi^(1/6),
    -4050^(1/6)/pi^(1/6),
    (-1/2-1/2*I*3^(1/2))*4050^(1/6)/pi^(1/6),
    (1/2-1/2*I*3^(1/2))*4050^(1/6)/pi^(1/6)

    LOL I got too many answers, no wonder why it says I'm a newbie.
    Last edited by LightEight; November 9th 2009 at 05:53 PM.
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