RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 18. Area of Circle, Sector and Segment

Subject: Maths - Class 10th

Q. No. 26 of Multiple Choice Questions (MCQ)

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26

In a circle of radius 14 cm, an arc subtends an angle of 120° at the centre. If √3 = 1.73 then the area of the segment of the circle is


Radius of Circle = R = 14 cm


Angle Subtended by the arc = θ = 120°


Area of sector subtending 120° = = 22/7 × 14 × 14 × 120/360 cm2


= 205.33 cm2


In Triangle ABC


AC = BC = 14 cm = R


Area of triangle ABC = 1/2 × base × height


= 2 × 1/2 × R sin θ/2 × R × cos θ/2


= 2 × 1/2 × 14 × 14 × sin 60° × cos 60°


= 84.77 cm2


Area of Segment = Area of sector subtending 120° - Area of triangle ABC


= 205.33 – 84.77 cm2 = 120.56 cm2

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