The surface area of a right-circular cone of radius r and height h is S = r

The surface area of a right-circular cone of radius r and height h is S = πr √r² + h², and its volume is V = 1/3 πr²h.
(a) Determine the ratio h/r for the cone with given surface area S and maximum volume V.
(b) What is the ratio h/r for a cone with given volume V and minimum surface area S ?
(c) Does a cone with given volume V and maximum surface area exist?