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A sector of $120^{°}$ cut out from a circle has an area of $9 \frac{3}{7}$ sq cm. What is the radius of the circle?

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3

2.5

3.5

3.6

answer is A.

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Detailed Solution

Given, area of an sector

= 9 \frac{3}{7}

sq. cm ,

θ = 120 °

.
Area of a sector

= \frac{θ}{360 °} \times π r^{2}

\Rightarrow \frac{θ}{360 °} \times π r^{2} = 9 \frac{3}{7}

\Rightarrow \frac{120 °}{360 °} \times \frac{22}{7} \times r^{2} = \frac{66}{7}

\Rightarrow r^{2} = \frac{66}{7} \times \frac{360^{o}}{120^{o}} \times \frac{7}{22} = 9

\Rightarrow r = \sqrt{9} = 3

cm
So, the radius of the circle is 3 cm.
Hence, option 1 is correct.

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