How is the surface area of a cone calculated?

The surface area of a cone is calculated by summing the area of its curved surface with the area of its circular base. The formula for the surface area includes two components: the lateral area (the area of the slanted surface) and the area of the base.

The lateral surface area of a cone is given by πrl, where r is the radius of the base and l is the slant height of the cone. To find the total surface area, you also need to add the area of the base, which is represented by πr².

Thus, by combining these two areas, the total surface area A can be expressed as:

[ A = \text{lateral area} + \text{base area} = \pi rl + \pi r^2 ]

This formula clearly depicts how both components contribute to the total surface area of the cone. Therefore, the provided correct choice appropriately represents this relationship.