Answer
(a) $-1.13cm/min$
(b) $-8.48cm/min$
Work Step by Step
Identify the given quantities: $\frac{dV}{dt}=-50m^3/min$, $r_0=45m, h_0=6m$
(a) With $V=\frac{1}{3}\pi r^2h$, $r/h=r+0/h_0=45/6, r=\frac{15}{2}h$, we have $V=\frac{1}{3}\pi (\frac{15}{2}h)^2h=\frac{75\pi}{4}h^3$ thus $\frac{dV}{dt}==\frac{225\pi}{4}h^2\frac{dh}{dt}$. With $\frac{dV}{dt}=-50m, h=5$, we get $\frac{dh}{dt}=\frac{-50(4)}{225\pi(5)^2}\approx-0.0113m/min=-1.13cm/min$
(b) $\frac{dr}{dt}=\frac{15}{2}\frac{dh}{dt}=-8.48cm/min$
