Question 316753
Imagine a cardboard tube.
Cut the tube lengthwise and unroll it. 
The tube is now unrolled and flattened into a rectangle.
The length of the rectangle is {{{h}}} along the cut line, {{{L=h}}}.
The width of the rectangle is the circumference of the circle or {{{C=2*pi*R}}}.
The area of the rectangle is 
{{{A=L*W=h*2*pi*R=2*pi*Rh}}}
Your surface area formula would only be correct if {{{h=R}}}
{{{R=1}}}
{{{h=4.5}}}
{{{A=2*pi*Rh=2*pi*1*4.5}}}
{{{A=9*pi}}} sq.in. or approximately,
{{{A=28.3}}} sq.in.