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

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Cone:

A right circular cone is a cone whose apex (top vertex of the cone) is perpendicular to the centre of the base of the circle.

Volume of a right circular cone:

Let

$'r'$ be the radius and

$'h'$ be the height of the cone.

Volume of a cone

$=$

$\frac{1}{3}$

$\times$ Volume of a cylinder

Volume of a cone

$=$

$\frac{1}{3} π r^{2} h$ cu. units

Example:

If the base radius is

$5 \ cm$ and the slant height is

$13 \ cm$ , find the volume of the cone.

$[$ Use

$\pi = 3.14]$

Solution:

Radius of the base

$=$

$5 \ cm$

Slant height

$=$

$13 \ cm$

Let us first find the height of the cone.

$l^2$

$=$

$r^2 + h^2$

$h^2$

$=$

$l^2 - r^2$

$h^2$

$=$

$13^2 - 5^2$

$h^2$

$=$

$169 - 25$

$h^2$

$=$

$144$

$h$

$=$

$12$

Height of the cone is

$12 \ cm$ .

Volume

$=$

$\frac{1}{3} π r^{2} h$ cu. units

$=$

$\frac{1}{3} \times 3.14 \times 5^{2} \times 12$

$=$

$314$

Therefore, the volume of the cone is

$314 \ cm^3$ .

Important!

The value of

$\pi$ should be taken as

$\frac{22}{7}$ unless its value is shared in the problem.

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3. Volume of right circular cone

Theory: