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    Question

    Consider a circle and a square whose circumference ratio

    is 11:8. If the sum of the circle's radius and the length of one side of the square equals 30 cm, determine the area of the circle.
    A 584 cm² Correct Answer Incorrect Answer
    B 454 cm² Correct Answer Incorrect Answer
    C 616 cm² Correct Answer Incorrect Answer
    D 1386 cm² Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let length of side of the square is ‘x’ cm Radius of the circle = ’30 – x’ cm According to question; [2 × 22/7 × (30 – x)]/(4x) = 11/8 8/7 × (30 – x) = x Or, 240 – 8x = 7x Or, 15x = 240 Or, x = 16 Radius of circle = 30 – 16 = 14 cm Desired Area = 22/7 × 14 × 14 = 616 cm2

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