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Math Help - volume of cilinder maximum problem. exam tmw!!!

  1. #1
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    volume of cilinder maximum problem. exam tmw!!!

    a cilindrical container of height h cm and radius r cm has both ends closed. It is produced using exactly 54pi cm2 of plastic.

    i) express h in terms of r
    ii) find the maximum possible volume of the container in terms of Pi.

    I did the first part, i need the steps for part ii)!
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  2. #2
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    Talking

    You have the formula for the volume V in terms of h and of r. You've solved for h in terms of r.

    Take the expression for h "in terms of r", and plug this in for "h" in the volume formula. This gives you the volume in terms only of r.

    Differentiate, etc.
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  3. #3
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    Hi, I`m new here but I think I can help

    The volume of the cylinder is given by the expression:

    V=\pi*r^2*h

    But, as you have h in terms of r, you can get:

    V=\pi\,r^2\,({54 \over 2r}-r)

    Now, if you derivate the above expression and equal it to 0 you can get the answer I think, I`ll do it and post it here.
    Last edited by Kuruma; April 19th 2009 at 04:09 AM.
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  4. #4
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    After a few calculations, I got a radius of 3, which leads us to a volume

    V=54\pi\,cm^3

    I`m not sure, but, if anyone wants to check it out...
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