How is the surface area of a cone calculated?

The surface area of a cone is comprised of two distinct components: the base area and the lateral area. The base of the cone is a circle, and its area can be calculated using the formula ( A = \pi r^2 ), where ( r ) is the radius of the base. The lateral area, which is the area around the sides of the cone, is calculated using the slant height ( l ). This leads to the formula for the lateral surface area being ( A = \pi r l ).

To find the total surface area of the cone, you combine both the base area and the lateral area, resulting in the formula:

[ SA = \pi r^2 + \pi r l ]

This total accounts for both the circular base and the cone's curved surface. Hence, the correct choice accurately reflects this formula, confirming that both components—base area and lateral area—are essential for determining the overall surface area of the cone.