Cone

A (right circular) cone is the set of all line segments joining a fixed point (the apex) to every point on a circle (the base) that lies in a plane not containing the apex. The axis of the cone is the line joining the apex to the center of the base. If the axis is perpendicular to the base, the cone is called a right cone.

Important properties

• The base is a circle with radius $r$.

• The height $h$ is the perpendicular distance from the apex to the base.

• The slant height $l$ is the distance from the apex to any point on the edge of the base.

• The volume of a cone is $V = \frac{1}{3}\pi r^2 h$.

• The lateral surface area is $A = \pi r l$.