small change from small changes

**s_ingram** · June 29th 2009, 03:44 PM

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

**pickslides** · June 29th 2009, 04:22 PM

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

$r=\sqrt( R^2-\frac{h^2}{4})$

**s_ingram** · June 30th 2009, 08:30 AM

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

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