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      Question

      Three circles, each having radius equal to 4 cm, are

      drawn with the vertices of an equilateral triangle as the centres. If the length of each side of the triangle is equal to 8 cm, then what is the area (in cm2) of the portion of the triangle that is NOT covered by the sectors of the circles?
      A 16(2√3 – Ο€) Correct Answer Incorrect Answer
      B 8(2√3 – Ο€) Correct Answer Incorrect Answer
      C 8(2√3 – Ο€/2) Correct Answer Incorrect Answer
      D 16(2√3 – Ο€/2) Correct Answer Incorrect Answer

      Solution

      Area of the triangle = √3/4 Γ— 82 = 16√3 cm2 Total area of the sectors of the circles that are lying on the triangle = 3 Γ— 60/360 Γ— Ο€ Γ— 42 = 8Ο€ cm2 Hence, required area = 16√3 - 8Ο€ = 8 (2√3 - Ο€) cm2

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