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SSC Quantitative Aptitude Mensuration Question Bank Mensuration-II (II)

  • question_answer
    If a hemisphere is melted and four spheres of equal volume are made, the radius of each sphere will be equal to       [SSC CGL Tier II. 2015]

    A) 1 /2 of the radius of the hemisphere

    B) 1/6th of the radius of the hemisphere

    C) 1/4th of the radius of the hemisphere

    D) radius of the hemisphere

    Correct Answer: A

    Solution :

    [a] Let the radius of hemisphere is R cm and the radius of each sphere is r cm. Then, according to the question, \[\frac{2}{3}\,\pi {{R}^{3}}=\frac{4}{3\,}\pi {{r}^{3}}\times 4\]\[\Rightarrow \]\[{{R}^{3}}=8{{r}^{3}}\]\[\therefore \]\[r=\frac{R}{2}\]


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