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 $\displaystyle \frac{4 \pi R^3}{3 \sqrt{3}}$

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

best regards