Question 882885
Yes.


Let h = height of cylinder


OPEN CYLINDER
{{{(2*pi*4)*h=10*pi}}}, {{{circumference*height=SurfaceAreaGiven}}}
{{{h=(10*pi)/(2*4*pi)}}}
{{{highlight(h=5/4)}}}


CLOSED CYLINDER
{{{(2*pi*4)h+2*(pi*4^2)=10pi}}}
{{{8*pi*h+32*pi=10pi}}}
{{{8h+32=10}}}
{{{8h=10-32<0}}} <b>Does Not Work</b>.


The description can work if the cylinder is open at both ends.  You can now figure if this will work for a cylinder open at only one end.