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Math Help - Derivative, some difficulties.

  1. #1
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    Derivative, some difficulties.

    Can someone please help me to solve this two problems? I've been sitting for hours trying to understand them.

    Here it goes.

    A 30 cm string was cut in two pieces. One string was formed as a circle and the second string was shaped as a quadrat.
    Show that the sum of the circle and the quadrat's area always exceed 30 cm² regardless where the cut is made.


    Found a third problem:


    A factory are going to to make cylindershaped cans. The sum of the diameter and height are 80 cm. which measures gives the greatest volume?

    Please help me with this!
    /Attack.
    Last edited by Attack; December 17th 2008 at 01:29 PM. Reason: Found a third problem!
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  2. #2
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  3. #3
    MHF Contributor
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    Hi

    Let x be the length of the string shaped as a circle
    x is the perimeter of the circle
    The radius is r = \frac{x}{2\pi}
    The area is A_c = \pi r^2 = \pi \frac{x^2}{4\pi^2} = \frac{x^2}{4\pi}

    The length of the other part of the string is 30-x
    30-x is the perimeter of the square
    The length of one side is a = \frac{30-x}{4}

    The area is A_s = a^2 = \frac{(30-x)^2}{16}

    The total area is A(x) = A_c + A_s = \frac{x^2}{4\pi} + \frac{(30-x)^2}{16}

    Just study the function A(x)

    EDIT : beaten again ! Arghh ....
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  4. #4
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    Well, thanks anyway, it was worth a shot.
    Last edited by ThePerfectHacker; December 18th 2008 at 08:59 PM.
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