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Thread: Problem

  1. #1
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    Joined
    Nov 2007
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    Problem

    A closed cylinder has a total surface area equal to $\displaystyle 600\pi$. Show that the volume,$\displaystyle V cm^3$, of this cylinder is given by the formula $\displaystyle V = 300\pi r - \pi r^3$, where $\displaystyle r cm$ is the radius of the cylinder.


    I only managed to get $\displaystyle V = 300\pi r$. Where have I gone wrong?

    Thanks in advanced.
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  2. #2
    Member
    Joined
    Aug 2007
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    $\displaystyle 2 \pi r^2 + 2 \pi rh = 600 \pi $

    $\displaystyle r^2 + rh = 300 $

    $\displaystyle V = \pi r^{2} h $

    $\displaystyle \pi r(r^2 + rh) = 300 \pi r $

    $\displaystyle \pi r^{2}h = 300 \pi r - \pi r^3 $
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