A cross-section of a river is a trapezoid with bases 10 and 16 and slanted sides of length 5 . At this section the water is flowing at $\pi \mathrm{mph}$. A little ways downstream is a dam where the water flows through 4 identical circular holes at $16 \mathrm{mph}$. What is the radius of the holes?
Solution: The volume of water going through any cross-section of the river in an hour (assuming the cross-sections are parallel) is the area times the velocity. The trapezoid has height 4 , hence area 52 , so the volume of water going through at any hour is $52 \pi$. Let $r$ be the radius of the holes, then the total area is $4 \pi r^{2}$, so the volume of water is $64 \pi r^{2}$. Therefore $64 \pi r^{2}=52 \pi$, so $r=\frac{\sqrt{13}}{4}$.