In a circle of radius 21 cm, an arc subtends an angle of 60° at the Centre. Find: (i) the length of the arc (ii) area of the sector formed by the arc (iii) area of the segment formed by the corresponding chord

Radius of circle = 21 cm
(i) The length of arc
= θ/360° × 2πr = 60°/360° × 2πr
= 1/6 × 2 × π × 21 = 1/6 × 2 × 22/7 × 21 = 22cm
(ii) Area of the sector formed by the arc
= 60°/360° × πr²
= 1/6 × π(21)²
= 1/6 × 22/7 × 21 × 21 = 231 cm²
(iii) Area of the segment formed by the corresponding chord
Area of sector – Area of △0AB
= 231 cm² – √3/4(21)²cm² [As triangle OAB is an equilateral triangle]
= 231 cm² – 441 √3/4cm²
= [231 – (441√3)/4]cm²

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