Question 85588
To find the surface area of the lateral side, we can "roll" out the lateral side like this



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So the area (which now represents a rectangle) is 


{{{2*pi*r*h}}}


the part {{{2*pi*r}}} represents the circumference of the circle at the top and the h is the height. So imagine the lateral surface area looking like this:


{{{drawing( 400, 300, -10, 10, -10, 10,
locate( -1, 6.5, 2*pi*r ),
locate( -6, 0, h ),
rectangle(-5,-5,7,5)
  )}}} Here is the lateral side rolled out


and here is the surface area of the top of the cylinder


{{{pi*r^2}}} which represents the area of a circle


So the surface area of the side and the top is:


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