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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 – π) Correct Answer Incorrect Answer
    B 8(2√3 – π) Correct Answer Incorrect Answer
    C 8(2√3 – π/2) Correct Answer Incorrect Answer
    D 16(2√3 – π/2) Correct Answer Incorrect Answer

    Solution

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

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