Question

    The diagonals of a rhombus are in the ratio 7:5, and its

    area is 3,500 cm². A circle is formed taking the smaller diagonal as the diameter. Find the difference between the area of the circle and three-fourths of the area of the rhombus. (Take π = 3)
    A 1124.1 cm² Correct Answer Incorrect Answer
    B 1580.4 cm² Correct Answer Incorrect Answer
    C 1310.2 cm² Correct Answer Incorrect Answer
    D 1391.2 cm² Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let diagonals = 7x and 5x

    Area = (1/2) × 7x × 5x = 17.5x²

    3500 = 17.5x² → x² = 200 → x = √200 ≈ 14.14

    Smaller diagonal = 5x ≈ 70.7 cm

    Radius ≈ 35.35 cm

    Area of circle ≈ 3 × (35.35)² ≈ 3 × 1249.7 ≈ 3749.1 cm²

    75% of rhombus = 0.75 × 3500 = 2625 cm²

    Difference ≈ 3749.1 - 2625 = 1124.1 cm²

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