Question

in circle of radius 21cm .an arc is subtends angle of 60 at the center

Answer 1

(i) Length of the arc AB = θ/360° × 2πr
                                        = 60°/360° × 2 × 22/7 × 21
                                        = 1/6 × 2 × 22/7 × 21 = 22

The length of the arc is  22 cm.

(ii) Angle subtend by the arc = 60° 

Area of the sector making angle 60° = (60°/360°) × π r2 cm2

                                          = (1/6) × 212π  = 441/6 π cm2
                               = 441/6 × 22/7 cm2 = 231 cm2
∴ Area of the sector formed by the arc is 231 cm2

(iii) Area of equilateral  ΔAOB = √3/4 × (OA)2 = √3/4 × 212 = (441√3)/4 cm2

Area of the segment formed by the corresponding chord 

                     = Area of the sector formed by the arc - Area of equilateral ΔAOB

                     = 231 cm2 - (441√3)/4 cm2