The surface area of a right-circular cone of radius $r$ and height $h$ is $S=\pi r\sqrt{r^2+h^2}$, and its volume is $V = \frac13\pi r^2h$.

(a) Determine $h$ and $r$ for the cone with given surface area $S=2$ and maximal volume $V$.
$h=$ ,$\quad$ $r=$

(b) What is the ratio $h/r$ for a cone with given volume $V=6$ and minimal surface area $S$?
$\frac{h}{r}=$

(c) Does a cone with given volume $V$ and maximal surface area exist?
A. yes
B. no