# Cone

Right circular cone is one whose axis is perpendicular to the plane of the base and it can be generated by revolving a right triangle about one of its legs.

## Surface area of a right circular cone

The surface area of a right circular cone is sum of the surface area of the bottom circle and the lateral surface area of a cone:

$$S=\pi r^{2} + \pi rl = \pi r(r+l)$$

where,

π— pi also referred to as Archimedes' constant is a mathematical constant, that is equal to the ratio of a circle's circumference to its diameter; It is approximately equal to 3.14159265359;
l— the slant height.

The surface area of a right circular cone is sum of the surface area of the bottom circle and the lateral surface area of a cone:

$$S=\pi r^{2} + \pi r\sqrt{r^{2}+h^{2}} = \pi r(r+\sqrt{r^{2}+h^{2}})$$

where,

h— the height.

## Slant height

The slant height of a right circular cone is the distance from any point on the circle of its base to the apex via a line segment along the surface of the cone. It can be found by Pythagorean theorem:

$$l=\sqrt{r^{2}+h^{2}}$$

## Volume of a right circular cone

$$V=\frac{1}{3}\pi r^{2} h$$

In addition to right circular cones there are oblique circular cones.