Question 66751
You are correct in what you have done so far.
Let's start with the volume of the cylindical pipe.
{{{(pi)r^2y = 600}}}  Substitute r here with: {{{r = x/2(pi)}}} from {{{x = 2(pi)r}}}
{{{(pi)(x/2(pi))^2y = 600}}} Simplify.
{{{(x^2/4(pi))y = 600}}} Now substitute the y here with {{{y = 1200/x}}} from the area, {{{xy = 1200}}}
{{{(x^2/4(pi))(1200/x) = 600}}} Simplify.
{{{1200x/4(pi) = 600}}} Multiply both sides by {{{4(pi)}}}
{{{1200x = 2400(pi)}}} Divide both sides by 1200.
{{{x = 2(pi)}}} and, from above:
{{{y = 1200/x}}}
{{{y = 1200/2(pi)}}}
{{{y = 600/(pi)}}}

The dimensions of the rectangular metal sheet are:
{{{2(pi)}}} by {{{600/(pi)}}} inches. or...using {{{(pi) = 3.14}}} as an approximation:
{{{2(3.14)}}} by {{{600/3.14}}} or 6.28 by 191.08 inches.