Well.....I could refer you to a "formula" page. But, let's think about this for a minute. Suppose that we consider a cylinder to be just a bunch of circles stacked on top of each other. Then, each circle would have a surface "area" equal to it's perimeter. i.e., 2 * Π * R, where R is the radius of the cylinder. Well, then the total surface area of the cylinder equals the "surface area" of each circle times the number of circles that we have. But the number of circles that we have just equals their total "height" which is the same height as the cylinder,
So the surface area of the cylinder is equal to:
("Area" of each circle) * (Height of cylinder) =
(2 * Π * R) * H =
2 * Π * R * H
And there you are......