# Math Help - small change from small changes

1. ## 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

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

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

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