Ex.12.2 Q1 Areas Related to Circles Solution - NCERT Maths Class 10

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Question

Find the area of a sector of a circle with radius \(6\,\rm{cm}\) if angle of the sector is \( {60^\circ}\).

Text Solution

What is known?

A circle with radius \(= 6 \,\rm{cm,}\) angle of the sector \( = {60^\circ}\)

What is unknown?

Area of sector of a circle.

Reasoning:

The formula for Area of the sector of angle \(\rm{\theta} \)

\[\begin{align}= \frac{\theta }{{360}} \times \pi {r^2}\end{align}\]

Steps:

\(\rm{\theta} = {60^\circ }\) Radius \(= 6\rm{}\,cm\)

\[\begin{align}\text{Area of the sector}&= \frac{\theta }{{360}} \times \pi {r^2}\\ &= \frac{{{{60}^o}}}{{{{360}^o}}} \times \frac{{22}}{7} \times 6 \times 6\\ &= \frac{{132}}{7}{\text{c}}{{\text{m}}^2}\\ &= 18\frac{6}{7}{\text{ c}}{{\text{m}}^2}\end{align}\]