Question 812451
The original 1600 in^2 piece has an x and a y length, each direction.  ONE of them would become a circumference and the other will become a cylinder length or height.


Cylinder volume would be {{{pi*r^2*h}}}, but we would also have some relation between h and the original sheet area {{{xy=1600}}}.  Let's use y as the cylinder height.  
{{{y=1600/x}}}, and if h=y, then
{{{pi*r^2*y=pi*r^2*(1600/x)=800}}}


What can we learn about r and x ?
Circumference, {{{2*pi*r=x}}}, because x is the other direction of the sheet, which becomes a circumference when the bending operation on the sheet is formed to make it into the cylinder.  Solve this circumf equation for r and substitute into the 800 volume equation:


{{{r=x/(2*pi)}}}.
{{{pi*r^2*(1600/x)=800}}}
{{{pi*(x/(2*pi))^2*(1600/x)=800}}}
{{{pi(x*x/(4*pi*pi))(1600/x)=800}}}
{{{(x*400/pi)=800}}}
{{{x=800*pi/400}}}
{{{highlight(x=2*pi)}}}


and now with x known, back to xy=1600 lets you find y.