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Find the area of the segment of a circle of radius $12 cm$ whose corresponding sector has a central angle of $60 °$ (Use $π = 3.14$ .

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8 c m^{2}

10.08 c m^{2}

13.08

c m^{2}

9 c m^{2}

answer is A.

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Detailed Solution

Given that, a circle of radius 12 cm whose corresponding sector has a central angle

60 °

.
Calculating the area of sector QAPB.

θ 360 π r 2 = 60360 × 227 × 122

Triangle is an isosceles triangle with

30 °, 60 °, 90 °

angles and it is a right angled triangle.
Let OM = h and MB = x.
Apply trigonometric ratios to find out the side.

\sin 6 0^{\circ} = \frac{Opposite}{Hypotenuse}

\Rightarrow

32 = h 12

\Rightarrow

63 cm

Apply trigonometric ratios to find out the sides

x

and AB.

\cos 60 ° = \frac{Adjacent}{Hypo tenuse}

\Rightarrow \frac{1}{2} = \frac{x}{12}

\Rightarrow x = 6

cm
AB = 2 MB

\Rightarrow

×

\Rightarrow

12 cm
Calculating the area of triangle QAB.

A r Δ O A B = 12 × B × H

⇒ 12 × A B × O M

⇒ 12 × 12 × 63

⇒ 62.35 c m 2

The area of line segment, subtract the Area of triangle OAB from the area of sector OACB.

75.43 − 6235 c m 2 = 13.08 c m 2

The area of the line segment of the circle is 13.08

{cm}^{2}

.
Hence the correct option is 1.

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