Answer
$x=2\pi\approx6.28in$ and $y=\frac{600}{\pi}\approx191in$
Work Step by Step
Step 1. Use the figure provided by the Exercise, with the given conditions, we can set up the following system of equations (let the radius of the cylinder be $r$):
\begin{cases} Area=xy=1200 \\ Volume=\pi r^2y=600\\Circumference=2\pi r=x \end{cases}
Step 2. Solve $r$ first by plug the first and third equations into the middle one:
$\pi r^2(\frac{1200}{2\pi r})=600$ which gives $r=1$ in
Step 3. We can find the other values as $x=2\pi\approx6.28in$ and $y=\frac{600}{\pi}\approx191in$
