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A circular disc of radius 10 cm is divided into sectors with angles $120^{\circ}$ and $150^{\circ}$ then the what is the ratio of the area of two sectors?

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4 : 5

5 : 4

2 : 1

8 : 7

answer is A.

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Detailed Solution

Given, a circular disc of radius 10 cm is divided into sectors with angles 120

°

and 150

°

.
Area of sector formed from angle

θ

\frac{θ}{360 °} π r^{2}

, where r is the radius of the circle.
Now, if angle is 120°, 150° then the ratio of areas of sector will be,

\Rightarrow

Required ratio =

\frac{\frac{120 °}{360 °} π r^{2}}{\frac{150 °}{360 °} π r^{2}}

\Rightarrow

Required ratio =

\frac{120}{150}

\Rightarrow

Required ratio

= 4 : 5

Hence, option 1 is correct.

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