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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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