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NTSE Sample Paper NTSE SAT Practice Test-9

  • question_answer
    A sphere of maximum volume is cut out from a solid hemisphere of radius r. The ratio of the volume of the hemisphere to that of the cut out sphere is

    A) 3 : 2                             

    B) 4 : 1

    C) 4 : 3                             

    D) 7 : 4

    Correct Answer: B

    Solution :

    [b] Volume of the hemisphere \[=\frac{2}{3}\pi {{r}^{3}}\] ....(i) Volume of the biggest sphere = volume of the sphere whose radius is \[\frac{r}{2}\] \[=\frac{4}{3}\,\,\pi {{\left( \frac{r}{2} \right)}^{3}}\]                ....(ii) From (i) and (ii) Required ratio \[=4:1.\]


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