How do you calculate the surface area of a cylinder?

The surface area of a cylinder is calculated by considering both its lateral surface area and the areas of its two circular bases. The formula includes two distinct parts: the lateral area, which is the curved surface that wraps around the cylinder, and the area of the circular bases.

The lateral surface area of a cylinder is given by the formula (2\pi rh), where (r) is the radius and (h) is the height. This calculates the area of the side of the cylinder as it can be visualized as a rectangle that is rolled into a circular shape.

In addition to the lateral surface area, the area of the two circular bases must be included. Each base has an area of (\pi r^2), so the combined area for both bases is (2\pi r^2).

When you add these two components together—(2\pi r^2) for the bases and (2\pi rh) for the lateral surface—you arrive at the total surface area of the cylinder, expressed as (2\pi r^2 + 2\pi rh).

Therefore, the choice providing the correct formula for the surface area of a cylinder effectively captures both aspects of the geometry