#### Answer

a. $(7.8,2000)$ and $(10,2000)$.
b. $(0,15)$

#### Work Step by Step

a. The solutions are the intersections of $y=200$ with the curve at $x=7.8\ in$ and $x=10\ in$, as indicated in the figure with points $(7.8,2000)$ and $(10,2000)$.
b. As volume needs to be positive, based on the graph, a realistic domain would be $0\lt x\lt 15\ in$ or $(0,15)$