A right circular cone with radius R and height H contains a liquid which evaporates at a rate proportional to its surface area in contact with air (proportionality constant $= \mathrm { k } > 0$ ). Find the time after which the cone is empty.
For every $\alpha \in \left( 0 , \frac { \pi } { 2 } \right)$, the value of $\sqrt { x ^ { 2 } + x } + \frac { \tan ^ { 2 } \alpha } { \sqrt { x ^ { 2 } + x } } , x > 0$ is greater than or equal to
A right circular cone with radius R and height H contains a liquid which evaporates at a rate proportional to its surface area in contact with air (proportionality constant $= \mathrm { k } > 0$ ). Find the time after which the cone is empty.