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    Question

    A cube of maximum possible volume is cut from a sphere

    of radius 5√3 cm. What is the ratio of the volume of a cube to that of the sphere?
    A 8: √3 π Correct Answer Incorrect Answer
    B 4: √3 π Correct Answer Incorrect Answer
    C 2: √3 π Correct Answer Incorrect Answer
    D 7: √3 π Correct Answer Incorrect Answer

    Solution

    Diagonal of cube = Diameter of sphere  √3 a = 2 (5√3)  ∴ a = 10 cm  Required ratio = volume of cube: volume of sphere = (10)³: 4/3 π (5√3)³  = 1000: 4/3 π × 125 × 3√3  = 2: √3 π  

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