### Theory:

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
Example:
Find the volume if the curved surface area of a right circular cylinder is $$660 \ cm^2$$ and the radius $$7 \ cm$$.

Solution:

Radius of the cylinder $$=$$ $$7 \ cm$$

Curved surface area $$=$$ $$660 \ cm^2$$

$$2 \pi rh$$ $$=$$ $$660$$

$2×\frac{22}{7}×7×h=660$

$h=660×\frac{7}{22×7×2}$

$$h$$ $$=$$ $$15$$

Height $$=$$ $$15 \ cm$$

Volume of the right circular cylinder $$=$$ $$\pi r^2 h$$ cu. units

$$=$$ $\frac{22}{7}×{7}^{2}×15$

$$=$$ $\frac{22}{7}×7×7×15$

$$=$$ $$2310 \ cm^3$$

Therefore, the volume of the cylinder is $$2310 \ cm^3$$.
Important!
The value of $$\pi$$ should be taken as $\frac{22}{7}$ unless its value is shared in the problem.