Question

A chord of a circle of radius 12cm subtends an angle of 120 at the centre .Find the area of corresponding segment of the circle .(pie = 3.14) and (root 3= 1.73)​

Answer 1

Answer:

Hence, the area of the corresponding segment of the circle is 88.44 cm².

Step-by-step explanation:

Given: Radius of circle = 12 cm   θ = 120°

Area of the segment= {(π/360) × θ - sin θ/2 cos θ/2} r²

Area of the segment={(π) × 120/360 - sin 120/2 cos 120/2 } 12²

= {(π) × ⅓ - sin 60° cos 60° } ×144

= (π/3 - ½ × √3/2) × 144

= (π/3 × 144 - 144 × √3/4

= 48π - 36√3

= 12(4π - 3√3)

= 12( 4 × 3.14 - 3 × 1.73)

[π = 3.14 , √3= 1.73]

= 12 (12.56 - 5.19)

= 12 × 7.37

= 88.44 cm²