Find the time required for an inverted conical tank of radius $\displaystyle R$ and height $\displaystyle H$ to empty through a round hole of cross sectional area $\displaystyle a$ at the bottom. Given that the water flows according to the formula $\displaystyle V(t) = k\sqrt{2gh(t)}$ where $\displaystyle V(t)$ and $\displaystyle h(t)$ are respectively the velocity of flow through the hole and the height of water level above the hole at time $\displaystyle t$ and $\displaystyle g$ is the acceleration due to gravity.