Area of a sector of central angle $120^o$ of a circle is $3\pi\ cm^2$. Then, find the length of the corresponding arc of this sector.


Given: Area of a sector of central angle $120^o$ of a circle is $3\pi\ cm^2$. 

To do: To find the length of the corresponding arc of this sector.

Solution:

Given angle is $120^o$ and area is $3\pi$



As known area of a sector $=\frac{\theta}{360^o}\pi r^2$

$\Rightarrow  3\pi =\pi  \times  r^2 \times \frac{120^o}{360^o}$

$\Rightarrow r^2=9$

$\Rightarrow r=\sqrt{9}$

$\Rightarrow r=3$

Length of the arc, $l=\frac{\theta}{360^o}\times 2\pi r$

$=\frac{120^o}{360^o}\times2\pi\times3$

$=2\pi$

Thus, length of the arc is $2\pi\ cm$.



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Updated on: 10-Oct-2022

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