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Math Help - Cylinder Optimization

  1. #1
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    Cylinder Optimization

    A cylindrical can hold 460 cubic centimeters of soup.
    Find the dimensions of the soup can that uses the least amount of material.

    I know that v=pi*(r^2)h and I have to optimize that by taking the derivative and setting equal to zero, but I'm not sure how to get h in terms of r. I had h=460/pi(r^2), but when I solved the problem it didn't turn out right. Maybe I'm doing something wrong?
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  2. #2
    Eater of Worlds
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    We have {\pi}r^{2}h=460

    Surface area is: S=2{\pi}rh+2{\pi}r^{2}

    Solve the volume equation for r or h, whatever.

    Then, sub into S. It will then be in terms of one variable. Differentiate, set to 0 and solve away.
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