Answer
$132183ft^3/hr$
Work Step by Step
Step 1. Without using calculus, we recall the formula for the area of an ellipse as $A=\pi (x/2)(y/2)$, where $x$ is the length of the major axis, and $y$ is the length of the minor axis.
Step 2. We are given that the thickness $z=9in=3/4ft, x=2 mi=10560ft, y=3/4mi=3960ft, x'=\frac{dx}{dt}=30ft/hr, y'=\frac{dy}{dt}=10ft/hr$
Step 3. Volume $V=3A/4=\frac{3\pi}{16}xy$, thus $\frac{dV}{dt}=\frac{3\pi}{16}(xy'+x'y)=\frac{3\pi}{16}(10560(10)+30(3960))\approx132183ft^3/hr$
