Question

    The height of a cone is equal to

    the height of a cylinder. The curved surface area of the cylinder is 616 cm², and the height of the cylinder is twice its radius. The radius of the cone is equal to half the radius of the cylinder. Quantity I: Calculate the difference between the total surface area and the curved surface area of the cylinder. Quantity II: Determine the curved surface area of the cone. Two quantities, Quantity I and Quantity II, are provided. Your task is to solve both quantities and determine the correct relationship between them. Choose the appropriate option.
    A Quantity-I > Quantity-II Correct Answer Incorrect Answer
    B Quantity I < Quantity II Correct Answer Incorrect Answer
    C Quantity I = Quantity II or No relation can be established Correct Answer Incorrect Answer
    D Quantity-I ≥ Quantity-II Correct Answer Incorrect Answer
    E Quantity-I ≤ Quantity-II Correct Answer Incorrect Answer

    Solution

    ATQ,

    Given:- CSA of the cylinder = 616 cm² Height of the cylinder = 2 × radius Radius of the cone = (1/2) × radius of the cylinder Find radius of the cylinder:

    Calculate Quantity I: TSA of cylinder = 924 cm² Difference = 924 - 616 = 308 cm² Calculate Quantity II: Radius of cone = 3.5 cm, slant height l=14.43 cm CSA of cone = 158.865 cm² Comparison: 308 > 158.865 Hence, Quantity I > Quantity II.

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