In a circle of radius \( 21 \mathrm{~cm} \), an arc subtends an angle of \( 60^{\circ} \) at the centre. Find area of the sector formed by the arc. (Use \( \pi=22 / 7 \) )

Given:

Radius of the circle $r=21 \mathrm{~cm}$.

Angle subtended by the arc $=60^{\circ}$

To do:

We have to find the area of the sector.

Solution:

We know that,

Area of the sector $=\pi r^{2} \times \frac{\theta}{360^{\circ}}$

Therefore,

Area of the sector formed by the arc$=\frac{22}{7}(21)^{2} \times \frac{60^{\circ}}{360^{\circ}}$

$=\frac{22}{7} \times 21 \times 21 \times \frac{1}{6}$

$=231 \mathrm{~cm}^{2}$

The area of the sector is $231 \mathrm{~cm}^{2}$. 

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Updated on: 10-Oct-2022

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