A sector is cut-off from a circle of radius $ 21 \mathrm{~cm} $. The angle of the sector is $ 120^{\circ} $. Find the length of its arc and the area.

Given:

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

Angle subtended by the arc $=120^{\circ}$

To do:

We have to find the length of the arc and area of the sector.

Solution:

Let the length of the arc be $l$.

We know that,

Length of arc $=2 \pi r(\frac{\theta}{360^{\circ}})$

Therefore,

Length of the arc $l=2 \times \pi \times 21 \times \frac{120^{\circ}}{360^{\circ}} \mathrm{cm}$

$=42 \pi \times \frac{1}{3} \mathrm{cm}$

$=14 \pi \mathrm{cm}$

$=14 \times \frac{22}{7} \mathrm{cm}$

$=44 \mathrm{~cm}$

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

$=\frac{22}{7}(21)^{2} \times \frac{120^{\circ}}{360^{\circ}}$

$=\frac{22}{7} \times 21 \times 21 \times \frac{1}{3}$

$=462 \mathrm{~cm}^{2}$

The length of the arc and area of the sector are $44 \mathrm{~cm}$ and $462 \mathrm{~cm}^{2}$ respectively. 

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Updated on: 10-Oct-2022

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