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      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 1580.4 cm² Correct Answer Incorrect Answer
      B 1310.2 cm² Correct Answer Incorrect Answer
      C 1124.1 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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