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

  • question_answer
    The capacities of two hemispherical bowls are 6.4 L and 21.6 L, respectively. Then, the ratio of their internal curved surface areas will be 

    A) 4 : 9

    B) 2 : 3

    C) \[\sqrt{2}:\sqrt{3}\]

    D) 16 : 81

    Correct Answer: A

    Solution :

    [a] Let the radius of hemispherical bowls be \[{{r}_{1}}\]and \[{{r}_{2}}\]respectively. According to the question, \[\frac{\frac{4}{3}\pi r_{1}^{3}}{\frac{4}{3}\pi r_{2}^{3}}=\frac{6.4}{21.6}\] \[\Rightarrow \]   \[\frac{r_{1}^{3}}{r_{2}^{3}}=\frac{64}{216}\]\[\Rightarrow \]\[\frac{{{r}_{1}}}{{{r}_{2}}}=\frac{4}{6}\]\[\Rightarrow \]\[{{r}_{1}}:{{r}_{2}}=2:3\] \[\therefore \]Ratio of their internal curved surface areas \[=\frac{2\pi r_{1}^{2}}{2\pi r_{2}^{2}}=4:9\]


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