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      Question

      In a circle of radius 7 cm, the area of a sector is 77

      cm². Find the angle of the sector and the length of its arc. (Take π = 22/7)
      A 18 cm Correct Answer Incorrect Answer
      B 22 cm Correct Answer Incorrect Answer
      C 28 cm Correct Answer Incorrect Answer
      D 32 cm Correct Answer Incorrect Answer

      Solution

      Area of sector = (θ/360) × πr² 77 = (θ/360) × (22/7) × 7² = (θ/360) × (22/7) × 49 = (θ/360) × 154 Thus θ/360 = 77/154 = 1/2 ⇒ θ = 180° Arc length = (θ/360) × 2πr = (180/360) × 2 × (22/7) × 7 = (1/2) × 2 × 22 = 22 cm.

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