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.
cone_3 (1).svg
Volume of a right circular cone:
Let \('r'\) be the radius and \('h'\) be the height of the cone.
 
Volume of a cone \(=\) 13 \(\times\) Volume of a cylinder
 
Volume of a cone \(=\) 13πr2h 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 \(=\) 13πr2h cu. units
 
\(=\) 13×3.143×52×12
 
\(=\) \(314.3\)
 
Therefore, the volume of the cone is \(314.3 \ cm^3\).
Important!
The value of \(\pi\) should be taken as 227 unless its value is shared in the problem.