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
1. Radius and 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:
$$S=\pi r^{2} + \pi rl = \pi r(r+l) $$
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;
r— the radius;
l— the slant height.
2. Radius and 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.
See also:
Frequently asked questions
How do you calculate the surface area of a cone?
The surface area of a cone equals the base area plus the lateral area.
What is the slant height of a cone?
The slant height is the distance from the rim of the base to the apex along the surface of the cone.
How do you calculate the volume of a cone?
The volume of a cone is one third of pi times radius squared times height.
