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Math Help - Calculate the diameter of a cylinder

  1. #1
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    Calculate the diameter of a cylinder

    Need to solve this but its hurting my head ...hehe

    Calculate the diameter of a cylinder. The cylinder has a spherical top and a flat circular base .
    The overall surface area is 2 M square.
    The total height is 84 cm ... Thats it. I can solve for regular cylinder but with a spherical top im stuck....SA for sphere is 4 pi r square so half that and H= H-R but bit stuck any help welcome ...

    Thanks
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  2. #2
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    Re: Calculate the diameter of a cylinder

    So this isn't really a cylinder, it is a cyinder with a hemispherical top. The surface are of the cylindrical part, which you say you can find, is 84\pi r^2 approximately. The flat base is a disk with radius r so has area \pi r^2. The surface of a sphere of radius r is 4\pi r^2 so the hemisphere is 2\pi r^2. That is, the "overall surface area" is 84\pi r^2+ \pi r^2+ 2\pi r^2= 87 \pi r^2= 2 square meters. Solve for r, in meters.
    Last edited by HallsofIvy; December 10th 2013 at 09:59 AM.
    Thanks from civil
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  3. #3
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    Re: Calculate the diameter of a cylinder

    Thanks for the post ..i have not explained properly .. I can solve for a normal cylinder to find r using quadratics , however this problem the overall height including the hemisphere is 84 cm ..therefore 84 pi r sq is wrong and so i cannot establish the radius ....more help required to establish the cylinder height ?
    Last edited by civil; December 10th 2013 at 10:29 AM. Reason: wrong
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  4. #4
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    Re: Calculate the diameter of a cylinder

    Okay, then the height of the cylinder is 84- r. Put that in where I had 84 before.
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  5. #5
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    Re: Calculate the diameter of a cylinder

    area of 1/2 sphere= 1/2pi d^2
    area of cylinder =pi(d)(0.84 - d/2)
    area of base= pi d^2/4
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