CYLINDER showing equations for area. The surface area of a cylinder is the area of the top and bottom plus the area of the wall. The area of the top is given by the formula for the area of a circle. So you need two of those (top + bottom). Then the area of the wall, which is the height (h) times the circumference (2?r). The volume of a cylinder is the area of the top times the height. This image shows the walls of the cylinder opening out to illustrate the derivation of the area equation. The cylinder sits on a white background making this image ideal for print work such as textbooks.