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Math Help - small change from small changes

  1. #1
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    Cool small change from small changes

    Hi guys,

    A cylinder of volume V is to be cut from a solid sphere of radius R. Prove that the max value of V is  \frac{4 \pi R^3}{3 \sqrt{3}}

    So, volume of cylinder V = \pi r^2 h and I have 4/3 \pi r^3 worth of material to play with and I guess we use the method of small changes i.e. \Delta y \approx \frac{dy}{dy} \Delta x but there doesn't seem enough info to get going. Can anyone help?

    best regards
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  2. #2
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    The radius of the cylinder (r) can be expressed in terms of the spheres radius (R) and the cylinder's height as

     r=\sqrt( R^2-\frac{h^2}{4})
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  3. #3
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    Thanks very much pickslides! One look at the formula and everything was clear.
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