The surface area of a cylinder is derived by adding up the area of the top, the area of the base and the area of the side. The base and the top are equal, so the area of one can be calculated then multiplied by 2.
The volume of any prism is calculated by multiplying the cross-sectional area by the height. The volume of a cube, for example, is equal to the area of the square base multiplied by the height of the cube. A cylinder is a circular prism, so its volume is the area of either the base or the top multiplied by the height of the cylinder.