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Ex 12.3, 14 - AB and CD are arcs of two concentric circles - Ex 12.3

  1. Chapter 12 Class 10 Areas related to Circles
  2. Serial order wise
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Ex 12.3, 14 AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O (see figure). If ∠AOB = 30°, find the area of the shaded region. Area of shaded region = Area of sector AOB – Area of sector COD Area of sector AOB radius = r = 21 cm & θ = 30° Area of sector AOB = 𝜃/360×πr2 = 30/360×22/7×21×21 = 1/12×22×3×21 = 231/2 cm2 Area of sector COD radius = r = 7 cm & θ = 30° Area of sector COD = 𝜃/360×πr2 = (30°)/360×22/7×(7)2 = 1/12×22/7×7×7 = 77/6 cm2 Now , Area of shaded region = Area of Sector OAB – Area of sector OCD = 231/2−77/6 = (3 × 231 − 77)/6 = (693 − 77)/6 = 616/6 = 308/3 cm2 Hence, area of shaded region = 308/3 cm2

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