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    Question

    The length of a rectangle is 4 cm more than the radius

    of a circle. The perimeter of the rectangle is 96 cm, and the ratio of its length to breadth is 8:4. Find the difference between the area of the circle and the area of the rectangle.
    A 2264 cm² Correct Answer Incorrect Answer
    B 1952 cm² Correct Answer Incorrect Answer
    C 2335 cm² Correct Answer Incorrect Answer
    D 2465 cm² Correct Answer Incorrect Answer

    Solution

    ATQ, Let the length and breadth of the rectangle be 8a cm and 4a cm, respectively. Perimeter of the rectangle = 2 × (Length + Breadth) 96 = 2 × (8a + 4a) 96 = 2 × 12a 96 = 24a a = 4 Length of the rectangle = 8a = 8 × 4 = 32 cm Breadth of the rectangle = 4a = 4 × 4 = 16 cm The radius of the circle = 32 − 4 = 28 cm Area of the circle = πr² = 22/7 × 28 × 28 = 2464 cm² Area of the rectangle = 32 × 16 = 512 cm² Required difference = 2464 − 512 = 1952 cm²

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