Surface Area of Cone

A cone is a three-dimensional shape that has a flat base, a curved surface, and a point at the top (apex). The flat base is circular in shape so that it has a radius. The height is the distance between the top and the base point.

Parts of a Cone

Vertices, Edges and Faces of a Cone

• A cone has 1 vertex.
• A cone has 1 edge.
• A cone has 2 faces (1 flat face and 1 curved surface).

Right Circular Cone

A right circular cone is a cone whose axis is perpendicular to the plane of the base, i.e., the line joining the midpoint of the circular base to the vertex of the cone forms a right angle with the circular base. The perpendicular height or simply the height of a cone is the perpendicular distance from the vertex to the base of the cone. The slant height of a right circular cone is the distance from the vertex to the circumference of the base.

Relation between slant height and height of a right circular cone:

The slant height of the cone of height h and radius r is given by

L = √(h²+ r² )

Area of a Cone

It has two kinds of surface area:
1. The curved surface area or the lateral surface area
2. Total surface area

Curved Surface Area of a Cone

It is also called the lateral surface area of the cone.
The curved surface area of a cone is the surface area of the lateral surface of the cone, excluding the base. It is the area of the curved part of the cone that makes up its sloping sides.

Curved Surface Area = πrL
Where r is the radius of the cone and L is the slant height of the cone.

Total Surface Area of a Cone

The total surface area of a cone is the sum of the area of its lateral surface and the area of its base.

The lateral surface area of a cone = πrL
The area of the base of a cone is given by the formula πr².

The total surface area of a cone = πrL + πr²
= πr(r + L)
Where r is the radius of the cone and L is the slant height of the cone.