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Question

A sector is cut from a circle of radius $$21$$ cm. The angle of the sector is $$150^o$$. Find the length of its arc and area.


A
27 cm and 412.7cm2
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B
36 cm and 436.9cm2
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C
45 cm and 517.5cm2
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D
55 cm and 577.5cm2
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Solution

The correct option is D $$55$$ cm and $$577.5cm^2$$

The length of arc $$l$$ and area $$A$$ of a sector of angle $$\theta$$ in a circle of radius $$r$$ are given by,

$$l=\displaystyle\frac{\theta}{360^o}\times 2\pi r$$

and $$A=\displaystyle\frac{\theta}{360^o}\times \pi r^2$$ respectively.

Here, $$r=21$$ cm and $$\theta=150^0$$

$$\therefore l = \dfrac{150}{360}\times2\times\dfrac{22}7\times21 = 55$$ cm

and 

$$A = \dfrac{150}{36}\times\dfrac{22}7\times21^2 = \dfrac{1155}2 = 577.5\ {cm}^2$$

Mathematics

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