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Q.

A chord of a circle of radius $12$ cm subtends an angle of $60 °$ at the centre. What is the area of the corresponding segment of the circle?

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a

{17.43 cm}^{2}

b

{13.08 cm}^{2}

c

{11.66 cm}^{2}

d

{9.64 cm}^{2}

answer is B.

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Detailed Solution

Given, a chord of a circle of radius

12

cm subtends an angle of

60^{°}

at the centre.
Question Image

Question Image

Here

r = 12 cm

,

θ = 60 °

.
Area of a sector =

\frac{θ}{360^{°}} \times π r^{2}

Area of the corresponding segment

ABXA

= [\frac{π r^{2} θ}{360} - \frac{1}{2} r^{2} sinθ]

\Rightarrow

Area of the corresponding segment

ABXA

= [\frac{3.14 \times 12 \times 12 \times 60^{o °}}{360^{°}} - \frac{1}{2} \times 12 \times \sin 60^{°}]

\Rightarrow

Area of the corresponding segment

BXA

= [\frac{314}{100} \times 12 \times 2 - 6 \times 12 \times \frac{\sqrt{3}}{2}] c m^{2}

.

[∵ \sin 60^{°} = \frac{\sqrt{3}}{2}]

\Rightarrow

Area of the corresponding segment

ABXA

= [\frac{7536}{100} - 36 \times 1.73] c m^{2}

\Rightarrow

Area of the corresponding segment

ABXA

= [75.36 - 62.28] c m^{2}

\Rightarrow

Area of the corresponding segment

ABXA

= {13.08 cm}^{2}

Hence, option 2 is correct.

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A chord of a circle of radius 12cm subtends an angle of 60° at the centre. What is the area of the corresponding segment of the circle?