The surface area of a cylinder is the sum of its top and bottom circles and its length portion. The formula to find the total area is A = 2(pi * r^2) + 2pi * r * h.
A cylinder consists of two circles of the same size and the cylindrical area between them. The cylindrical area is essentially a rectangle curved in the third dimension. The formula to find the area of a circle is A = pi r^2, and for a rectangle, the formula is A = width * height. In a cylinder, the width of the rectangle is represented by the perimeter of the top circle, or 2pi * r. The expanded formula is represented by A = (pi * r^2) + (pi * r^2) + (2pi * r * h).