# Math Help - Differentiation Applications Problem

1. ## Differentiation Applications Problem

A solid right circular cylinder has a hemisphere hollowed out from each end. Given that the total surface area is 64pi cm sq, find the radius of the cylinder when the volume is maximum.

2. Originally Posted by puggie
A solid right circular cylinder has a hemisphere hollowed out from each end. Given that the total surface area is 64pi cm sq, find the radius of the cylinder when the volume is maximum.
Surface area
$2\pi r^2+2\pi rh-6\pi r^2=64\pi$ simplifies to ..

$h=\frac{32+2r^2}{r}$

Volume ..

$V=\pi r^2h-\frac{4}{3}\pi r^3$

Substitute h into this equation . After that , calculate $\frac{dV}{dr}$ then have it equals to 0 to find r .