How do you calculate the surface area of a right circular cone?

The surface area of a right circular cone is determined by adding the area of its base to the area of its lateral surface.

The base of the cone is a circle, and its area can be calculated using the formula πr², where r is the radius of the base.

The lateral surface area of the cone can be calculated using the formula πr√(r² + h²). Here, r is again the radius, and h is the height of the cone. The term √(r² + h²) represents the slant height of the cone, which forms the hypotenuse of a right triangle made up of the radius, height, and the slant height.

Thus, to find the total surface area of the cone, you combine both parts: the area of the base and the lateral surface area. This leads to the formula SA = πr² + πr√(r² + h²), which accurately represents the surface area of a right circular cone.

In this context, the correct answer captures both necessary components, providing a complete formula to calculate the surface area effectively.