Question 765577
 The surface area of a cylinder can be found by breaking it down into three parts:

    The two circles that make up the ends of the cylinder.
    The side of the cylinder, which when "unrolled" is a rectangle
The area of the rectangle is the width times height.

The area of a circle is {{{r^2*pi}}}, so the combined area of the two disks is twice that, or {{{2r^2*pi}}}. 

The width is the height {{{h}}} of the cylinder, and the length is the distance around the end circles. 

This is the circumference of the circle and is {{{2*pi*r}}}. Thus the rectangle's area is {{{2*pi*r * h}}}.

so, {{{SA=2r^2*pi+2*pi*r * h}}}

since your  cylinder  does not have a top, the surface area will be

 {{{SA=r^2*pi+2*pi*r * h}}}

if your {{{a=r=2cm}}} and {{{b=h =9cm}}}, then we have


{{{SA=(2cm)^2*3.142+2*3.142*2cm *9cm}}}


{{{SA=4cm^2*3.142+6.284*18cm^2}}}


{{{SA=12.568cm^2+113.112cm^2}}}


{{{SA=125.68cm^2}}}