Right circular cylinder:
A cylinder whose bases are circular in shape and the axis joining the two centres of the bases perpendicular to the planes of the two bases is called a right circular cylinder.
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
Find the volume if the curved surface area of a right circular cylinder is \(660 \ cm^2\) and the radius \(7 \ cm\).
Radius of the cylinder \(=\) \(7 \ cm\)
Curved surface area \(=\) \(660 \ cm^2\)
\(2 \pi rh\) \(=\) \(660\)
\(h\) \(=\) \(15\)
Height \(=\) \(15 \ cm\)
Volume of the right circular cylinder \(=\) \(\pi r^2 h\) cu. units
\(=\) 227×72×15
\(=\) 227×7×7×15
\(=\) \(2310 \ cm^3\)
Therefore, the volume of the cylinder is \(2310 \ cm^3\).
The value of \(\pi\) should be taken as 227 unless its value is shared in the problem.