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If a sector of a circle of diameter $21 cm$ subtends an angle of $120^{\circ}$ at the center, then what is its area?

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115.5 c m^{2}

84 c m^{2}

85.5 c m^{2}

78 c m^{2}

answer is A.

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Detailed Solution

It is given that, sector of a circle of diameter

21 cm

subtends an angle of

120^{\circ}

at the center.
We know that,
Area of sector

= \frac{θ}{360} \times π r^{2}

. Here,

θ = 120 ° and Diameter = 21 cm

\Rightarrow r = \frac{21}{2} cm

Therefore,

Area = \frac{120}{360} \times π \times {(\frac{21}{2})}^{2}

\Rightarrow Area = \frac{1}{3} \times \frac{22}{7} \times \frac{441}{4}

\Rightarrow Area = 115.5 c m^{2}

Therefore, area of the sector is

115.5 c m^{2}

.
Hence, option (1) is correct.

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