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Math Help - surface area/volume of cylinder

  1. #1
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    surface area/volume of cylinder

    The volume of a solid cylinder is 128\pi cm^{3}.
    Show that the total surface area, A cm^{2}, is A=2\pi r^{2}+\frac{256\pi}{r} where r>0.


    Anyway if anybody could please help me with this question I will be eternally grateful!
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  2. #2
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    e^(i*pi)'s Avatar
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    Volume of a cylinder: V = \pi r^2 h

    Surface area of a cylinder: A = 2\pi r^2 + 2\pi r h

    ================================================== =========================

    In your case: V = \pi r^2h = 128\pi

    Rearrange to make h the subject (because it will need to be eliminated): h = \dfrac{128}{r^2}


    Sub the above expression for h into the equation for A at the top of the post and simplify
    Last edited by e^(i*pi); December 1st 2010 at 06:33 AM. Reason: improve clarity and leave the OP something to do
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  3. #3
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     V=\pi r^2h

     h=\frac{128}{\pi r^2}=\frac{128}{r^2}

     A=2\pi r^2 +2\pi rh
     =2\pi r^2 +2\pi r(\frac{128}{r^2})
     A = 2\pi r^2+\frac{256\pi}{r}
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