Question 1201847
<br>
Let x be the width of the piece of sheet metal, and let y be its length.<br>
Roll the sheet lengthwise to form the cylinder; the height of the cylinder is x and the circumference of the cylinder is y.  Then the radius of the cylinder is circumference divided by 2pi, or y/(2pi).<br>
Then<br>
[1] {{{xy = 1200}}}  [the area of the piece of sheet metal is 1200 sq in]
[2] {{{(pi)x(y^2/(4pi^2))=600}}}  [the volume of the cylinder ({{{(pi)(r^2)h}}}) is 600 cu in]<br>
Substitute [1] in [2]:<br>
{{{(pi)(xy)(y)/(4pi^2)=600}}}
{{{(pi)1200(y)/(4pi^2)=600}}}
{{{2y/(4pi)=1}}}
{{{2y=4pi}}}
{{{y=2pi}}}<br>
Substitute that in [1] to find x:<br>
{{{x(2pi)=1200}}}
{{{x=600/pi}}}<br>
ANSWERS:
width: {{{x=600/pi}}}
length: {{{y=2pi}}}<br>
You can evaluate those dimensions and do the rounding....<br>