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    Question

    The radius of a sphere is 75% of the radius of a

    cylinder, while the height of the cylinder is 25% greater than its radius. Determine the ratio of the volume of the sphere to that of the cylinder.
    A 9:20 Correct Answer Incorrect Answer
    B 11:20 Correct Answer Incorrect Answer
    C 3:20 Correct Answer Incorrect Answer
    D 3:5 Correct Answer Incorrect Answer
    E 3:4 Correct Answer Incorrect Answer

    Solution

    Let the radius of the cylinder be '4a' units. So, the height of the cylinder = 4a X (5/4) = '5a' units Radius of the sphere = 4a X 0.75 = '3a' units Volume of the sphere = (4/3) X π X radius3 Volume of the cylinder = π X radius2 X height Therefore, required ratio = ((4/3) X π X radius3) :(π X radius2 X height) = [(4/3) X π X (3a) 3]:[π X (4a) 2 X 5a] = 36:80 = 9:20

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