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      Question

      The length of a rectangle exceeds the radius of a circle

      by 3 cm. The perimeter of the rectangle is 72 cm, and the ratio of its length to breadth is 6:3. Find the difference between the area of the circle and the area of the rectangle.
      A 2264 cm² Correct Answer Incorrect Answer
      B 1098 cm² Correct Answer Incorrect Answer
      C 2335 cm² Correct Answer Incorrect Answer
      D 2465 cm² Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ, Let the length and breadth of the rectangle be 6a cm and 3a cm, respectively. Perimeter of the rectangle = 2 × (Length + Breadth) 72 = 2 × (6a + 3a) 72 = 2 × 9a 72 = 18a a = 4 Length of the rectangle = 6a = 6 × 4 = 24 cm Breadth of the rectangle = 3a = 3 × 4 = 12 cm The radius of the circle = 24 − 3 = 21 cm Area of the circle = πr² = 22/7 × 21 × 21 = 1386 cm² Area of the rectangle = 24 × 12 = 288 cm² Required difference = 1386 − 288 = 1098 cm²

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