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    Question

    A rhombus has an area of 1,800 cm², and its diagonals are

    in the ratio 6:5. A circle is drawn using the smaller diagonal as its diameter. What is the difference between the area of the circle and 75% of the area of the rhombus? (Take π = 3)
    A 724.1 cm² Correct Answer Incorrect Answer
    B 580.4 cm² Correct Answer Incorrect Answer
    C 897.9 cm² Correct Answer Incorrect Answer
    D 1091.2 cm² Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let diagonals = 6x and 5x

    Area = (1/2) × 6x × 5x = 15x²

    1800 = 15x² → x² = 120 → x = √120 ≈ 10.95

    Smaller diagonal = 5x ≈ 54.75 cm

    Radius ≈ 27.375 cm

    Area of circle ≈ 3 × (27.375)² ≈ 3 × 749.3 ≈ 2247.9 cm²

    75% of rhombus = 0.75 × 1800 = 1350 cm²

    Difference ≈ 2247.9 - 1350 = 897.9 cm²

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