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#1

$Old$ June 29th, 2009, 05:44 PM

s_ingram $s_ingram is offline$

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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?

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$Old$ June 29th, 2009, 06:22 PM

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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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$Old$ June 30th, 2009, 10:30 AM

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Thanks very much pickslides! One look at the formula and everything was clear.

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