In elementary geometry, cones are assumed to be right circular, where right means that the axis passes through the centre of the base at right angles to its plane, and circular means that the base is a circle. A right circular cone is obtained when one base of a right circular cylinder is shrunk to a point, vertex. The radius of the base is represented by 'r', and 'h' is the height of a cone. The variable 'l' is used to represent the slant height, which is the distance from a point on the circumference of the base to the vertex.

Volume of a Right Circular Cone

A right circular cone is a cone whose axis is a line segment joining the vertex to the midpoint of the circular base. The volume of a cone is one third of the product of the area of base and the height of the cone. The volume of the cone depend upon the area of base and height of the cone. The volume of a right circular cone is expressed in cubic units.

Formula:

Volume of a Cone =
$\frac{1}{3}$$\pi r^2h Where, r = Radius of the cone h = Height of the cone. Surface Area of a Right Circular Cone The surface area of a cone is the product of \pi, radius of the cone (r) and its slant height (l). The surface area of a right circular cone is the sum of area of base of a cone and surface area of a cone. The surface area is expressed in square units. The lateral surface area of a right circular cone is SA = \pi rl Where l = \sqrt{r^2 + h^2} The surface area of the bottom circle with radius 'r' of a cone is the same as for any circle, \pi r^2. Thus the total surface area of a right circular cone is: SA = \pi r^2 + \pi rl or SA = \pi r(r + l) Formula: Surface Area of a Cone = \pi r(r + l) Here, l = \sqrt{ r^2 + h^2} Where, 'r' be the radius, 'h' be the height and 'l' be the slant height of a cone. Frustum of a Right Circular Cone A frustum may be formed from a cone with a circular base by cutting off the tip of the cone and upper and lower bases that are circular and parallel. A frustum of a right circular cone with height h, lower base radius R, and top radius r is given below: Formulas: Volume = \frac{1}{3}$$\pi$h($r^2 + rR + R^2$)

Lateral Surface Area = $\pi$ l (r + R)

Total Surface Area = $\pi$[r(r + l) + R(R + l)]

Here, l = $\sqrt{[(R - r)^2 + h^2] }$

Where,
r = Small radius (Radius of top circle)
R = Large circle (Radius of base of frustum of a cone)
h = Height
l = Slant height.