Answer
$2\pi$ in $\times$ $\frac{600}{\pi}$ in
Work Step by Step
Let $x$ in and $y$ in be the length and width of the rectangular metal.
Since the area of the metal is 1200 in$^2$, we have
$xy=1200$
Since the volume of the cylindrical stovepipe is 600 in$^3$, we have
$V=\pi\cdot radius^2\cdot height$ (Note that $radius=\frac{perimeter}{2\pi}$)
$V=\pi \cdot (\frac{x}{2\pi})^2\cdot y$
$600=\frac{1}{4\pi}x^2y$
$x^2y=2400\pi$
Now, the system corresponding to the problem is given by:
$xy=1200$
$x^2y=2400\pi$
Substituting the first equation to the second one,
$x\cdot xy=2400\pi$
$x\cdot 1200=2400\pi$
$x=2\pi$
Then, $y=\frac{1200}{x}=\frac{1200}{2\pi}=\frac{600}{\pi}$
Therefore, the sheet metal has the dimensions $2\pi$ in $\times$ $\frac{600}{\pi}$ in.
