(Solved): A hemispherical water tank is being filled with water at a constant rate. The volume of the filled ...

A hemispherical water tank is being filled with water at a constant rate. The volume of the filled portion, as shown in the cross sectional diagram, is $$V=?h^2\left(R?\frac{1}{3}h\right)$$ Suppose the radius of the tank is 7.5 feet, and it is being filled at a rate of 60 cubic feet per hour. At the instant when $$h=2.8$$ feet, compute the following values. All answers must be accurate to 2 decimal places and include correct units. $$\begin{array}{ll}V=& \frac{dV}{dt}=\\ R=& \frac{dR}{dt}=\\ h=& \frac{dh}{dt}=\end{array}$$ At the instant when $$h=2.8$$ feet, how fast is the water level rising? [Hint: the answer is in one of the boxes above.]