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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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