Book: RS Aggarwal - Mathematics
Chapter: 18. Area of Circle, Sector and Segment
Subject: Maths - Class 10th
Q. No. 26 of Multiple Choice Questions (MCQ)
Listen NCERT Audio Books to boost your productivity and retention power by 2X.
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
