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Math Help - Work done emptying a cylindrical tank

  1. #1
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    Work done emptying a cylindrical tank

    I keep getting negative answers for this problem, so I was wondering if it can even be solved using the method taught in Calc. 1/2. We're supposed to first find volume, then force, when work, and then take the integral of the work.

    A tank is in the shape of a cylinder lying on its side The cylinder is 10 feet long and 5 feet in diameter. It is filled with a liquid which has a density of 90 pounds per cubic foot. Find the work done emptying the tank through a spout that rises 1 foot above the top of the tank.
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  2. #2
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    W=2\sqrt{(\frac{5}{2})^{2}-x^{2}}

    W=\int_{-\frac{5}{2}}^{\frac{5}{2}}\left(\frac{7}{2}-x\right)(90)\left(2\sqrt{(\frac{5}{2})^{2}-x^{2}}\right)(10)dx
    Attached Thumbnails Attached Thumbnails Work done emptying a cylindrical tank-cylinder-work.gif  
    Last edited by galactus; October 3rd 2009 at 02:00 AM.
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  3. #3
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    The first equation ...

    I know that the formula for a circle is r^2 = (y-b)^2 + (x-a)^2 . Why are you squaring r twice?
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  4. #4
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    Quote Originally Posted by laura35066 View Post
    I know that the formula for a circle is r^2 = (y-b)^2 + (x-a)^2 . Why are you squaring r twice?
    consider it a typo ... it happens.
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  5. #5
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    Yes, that is a typo. Thanks Skeeter.
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