The answer is approximate. Use more decimal digits of pi to get a more accurate answer (though it will never be exact unless you leave it in terms of pi).
The portion 2pi*r^2 is the fact we have two circular bases with area of pi*r^2 each.
The portion 2*pi*r*h is the lateral area, or the area around the curved side. If you unfold this portion, as you would maybe a label on a soup can, it has base of 2*pi*r and height h. The base 2pi*r is the circumference of the circle of radius r.
