### Theory:

Cone:
A right circular cone is a cone whose apex (top vertex of the cone) is perpendicular to the centre of the base of the circle.
Volume of a right circular cone:
Let $$'r'$$ be the radius and $$'h'$$ be the height of the cone.

Volume of a cone $$=$$ $\frac{1}{3}$ $$\times$$ Volume of a cylinder

Volume of a cone $$=$$ $\frac{1}{3}\mathrm{\pi }{r}^{2}h$ cu. units
Example:
If the radius of the base is $$5 \ cm$$ and slant height is $$13 \ cm$$, find the volume of the cone.

$$[$$Use $$\pi = 3.143]$$

Solution:

Radius of the base $$=$$ $$5 \ cm$$

Slant height $$=$$ $$13 \ cm$$

Let us first find the height of the cone.

$$l^2$$ $$=$$ $$r^2 + h^2$$

$$h^2$$ $$=$$ $$l^2 - r^2$$

$$h^2$$ $$=$$ $$13^2 - 5^2$$

$$h^2$$ $$=$$ $$169 - 25$$

$$h^2$$ $$=$$ $$144$$

$$h$$ $$=$$ $$12$$

Height of the cone is $$12 \ cm$$.

Volume $$=$$ $\frac{1}{3}\mathrm{\pi }{r}^{2}h$ cu. units

$$=$$ $\frac{1}{3}×3.143×{5}^{2}×12$

$$=$$ $$314.3$$

Therefore, the volume of the cone is $$314.3 \ cm^3$$.
Important!
The value of $$\pi$$ should be taken as $\frac{22}{7}$ unless its value is shared in the problem.