# Cone

A **cone** (or *circular cone*) is a three-dimensional solid. It consists of a circular base, a point (called the *vertex*), and all the points that lie on line segments connecting the vertex to the base. Thus, the cone is the special case of the pyramid in which the base is circular.

## Important terminology

The distance from the vertex to the plane containing the base is the *height* of the cone, and is frequently denoted . The radius of the base is called the radius of the cone and is frequently denoted . If the vertex lies directly above the center of the base, we call the cone a * right circular cone* (or

*right cone*for short). In this case, the vertex is the same distance from every point on the boundary of the base; this distance is called the

*slant height*of the cone, and is sometimes denoted or . If a cone is not a right cone (that is, if the vertex is not directly above the center of the base), we call it an

*oblique cone*.

## Properties

- A cone with radius and height has volume . This is a special case of the general formula for the volume of a pyramid, , where is the volume, is the area of the base and is the height.
- A right cone of radius and slant-height has surface area (the lateral area is , and the area of the base is ).

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