Volume of right circular cone — lesson. Mathematics CBSE, Class 9.

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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 radius of the base is \(5 \ cm\) and slant height is \(13 \ cm\), find the volume of the cone.

\([\)Use \(\pi = 3.143]\)

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 3.143 \times 5^{2} \times 12

\(=\) \(314.3\)

Therefore, the volume of the cone is \(314.3 \ cm^3\).

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 cone