Theory:

Right circular cylinder:
A cylinder whose bases are circular inshape and the axis joining the two centres of the bases perpendicular to the planes of the two bases is called a right circular cylinder.
right_cylinder.png
Volume of a right circular cylinder:
Let \('r'\) be the base radius and \('h'\) be the height of the cylinder.
 
Volume \(=\) Base area \(\times\) Height cu. units
 
Volume \(=\) Area of circle\(\times\) Height cu. units
 
Volume \(=\) \(\pi r^2 \times h\) \(=\) \(\pi r^2 h\) cu. units
Example:
If the curved surface area of a cylinder is \(660 \ cm^2\) and radius \(7 \ cm\), find its volume.
 
Solution:
 
Radius of the cylinder \(=\) \(7 \ cm\)
 
Curved surface area \(=\) \(660 \ cm^2\)
 
\(2 \pi rh\) \(=\) \(660\)
 
2×227×7×h=660
 
h=660×722×7×2
 
\(h\) \(=\) \(15\)
 
Height \(=\) \(15 \ cm\)
 
Volume of the cylinder \(=\) \(\pi r^2 h\) cu. units
 
\(=\) 227×72×15
 
\(=\) 227×7×7×15
 
\(=\) \(2310 \ cm^3\)
 
Therefore, the volume of the cylinder is \(2310 \ cm^3\).
Important!
The value of \(\pi\) should be taken as 227 unless its value is shared in the problem.