Volume of right circular cylinder — lesson. Mathematics State Board, Class 10.

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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.

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1. Volume of right circular cylinder

Theory: