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      Question

      Find the curved surface area of a right circular cone

      with a radius of 40 cm. The height of the cone is one-third of the length of a rectangle. The rectangle has a perimeter of 96 cm and a breadth of 21 cm. Round off the final answer to the nearest integer, using π = 22/7.
      A 5,484 cm² Correct Answer Incorrect Answer
      B 4,836 cm² Correct Answer Incorrect Answer
      C 4,972 cm² Correct Answer Incorrect Answer
      D 5,154 cm² Correct Answer Incorrect Answer
      E 4,692 cm² Correct Answer Incorrect Answer

      Solution

      Length of rectangle = (96/2) - 21 = 48 - 21 = 27 cm

      Height of cone = (1/3) X 27 = 9 cm

      Now, slant height of cone = √(height 2 + radius 2 ) = √(9 2 + 40 2 )

      = √(81 + 1600) = √1681 = 41 cm

      Curved surface area of cone = π X radius X slant height

      = (22/7) X 40 X 41 ~ 5,154 cm 2

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