A large cone$-$shaped container $($height H and radius R$)$ is fed a liquid solution of density $\backslash$rho at a

constant flow rate q$0.$ The solution evaporates from its top surface exposed to the sun.

$($a$)$ Assuming that the rate of evaporation is proportional to the area of the surface with a

constant K $($kg$/$m$2.$s$),$ develop a differential equation for the variation with time of the level of

the liquid in the container.

$($b$)$ What should be the feed flow rate to maintain the fluid level constant once it reaches a

desired value h$*?$

$($c$)$ If the feed was zero, would the rate of change of the level of the fluid depend on the shape

of the container?