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    Question

    A square PQRS is inscribed inside

    a circle. Another circle is inscribed within the square PQRS, and this process repeats infinitely. If the radius of the initial circle is 6 cm, what is the sum of the areas of all the circles?
    A 25π Correct Answer Incorrect Answer
    B 72π Correct Answer Incorrect Answer
    C 65π Correct Answer Incorrect Answer
    D 45π Correct Answer Incorrect Answer

    Solution

    ATQ,

    Diameter of the first circle = 2×6 = 12. The side of the square PQRS = Diameter of the second circle =12/√2 Area of the first circle = 36π. Sum of areas of circles =  

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