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Thread: surface area/volume of cylinder

  1. #1
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    surface area/volume of cylinder

    The volume of a solid cylinder is $\displaystyle 128\pi cm^{3}$.
    Show that the total surface area, $\displaystyle A cm^{2}$, is $\displaystyle A=2\pi r^{2}+\frac{256\pi}{r}$ 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: $\displaystyle V = \pi r^2 h$

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

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

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

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


    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); Dec 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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    $\displaystyle V=\pi r^2h$

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

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