Chapter 6, Problem 11P

(a)

To determine

To show: The volume V as a function of height of water h.

(b)

To determine

To show that: The rate of change of volume as $\frac{dV}{dt}=\pi {\left[f\left(h\right)\right]}^2\frac{dh}{dt}$.

(c)

To determine

The formula for the function f such that $\frac{dh}{dt}$ is a constant C.

To show: The advantage, if $\frac{dh}{dt}=C$.