The surface area of a cone is the sum of the curved surface area and the base area. The curved surface area of a cone is the lateral area, which is the area of the cone excluding the base. The base area of a cone is simply the area of the circle that forms its base.

Real-life examples of cones include traffic cones, ice cream cones, and the shape of a volcano. Calculating the surface area of a cone is useful in various fields, such as engineering, architecture, and construction. For example, when designing a traffic cone, the surface area is important to ensure the cone is visible and stable. In architecture, the surface area of a cone-shaped roof is considered to determine the amount of materials needed for construction.

The formula for determining the surface area of a cone is defined as: