2017 RI P1 Q2

A right circular cone has base radius \(r\) cm and height \(h\) cm. As \(r\) and \(h\) vary, its curved surface area, \(\pi r\sqrt{\left( {{r}^{2}}+{{h}^{2}} \right)}\) cm\(^{2}\), remains constant.

It is given that when \(r=\sqrt{2}\) cm, the magnitude of the rate of change of \(h\) is 10 times the magnitude of the rate of change of \(r\). Given also that \(h>r\), find the height of the cone at this instant.[4]