UPSKILL MATH PLUS

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Learn more### 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 \(=\) \(660 \ cm^2\)

\(2 \pi rh\) \(=\) \(660\)

$2\times \frac{22}{7}\times 7\times h=660$

$h=660\times \frac{7}{22\times 7\times 2}$

\(h\) \(=\) \(15\)

Height \(=\)

**\(15 \ cm\)**Volume of the right circular cylinder \(=\) \(\pi r^2 h\) cu. units

\(=\) $\frac{22}{7}\times {7}^{2}\times 15$

\(=\) $\frac{22}{7}\times 7\times 7\times 15$

\(=\) \(2310 \ cm^3\)

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.