(Solved): The hemispherical tank of radius 2m, shown above, is initially full of water at 50F. It is hea ...

The hemispherical tank of radius $2\mathrm{m}$, shown above, is initially full of water at $50^{?}\mathrm{F}$. It is heated with a constant heat source of $400^{?}\mathrm{F}$. After $5\min$, the temperature of the water is $100^{?}\mathrm{F}$. When the water reaches $212^{?}\mathrm{F}$, a valve of radius $1\mathrm{cm}$ is opened at the bottom and the water drains out. How long does it take for the tank to heat to the required temperature and completely drain?