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

  • question_answer
    Assume that a drop of water is spherical and its diameter is one-tenth of 1 cm. A conical glass has   height equal to the diameter of its rim. If 32000 drops of water fill the glass completely, then the  eight of the glass, (in cm) is

    A) 1

    B) 2

    C) 3

    D) 4

    Correct Answer: D

    Solution :

    [d] Given diameter of the water drop\[=\frac{1}{10}\,cm\] Hence radius of the water drop \[=\frac{\text{Diameter}\,\text{of}\,\text{water}\,\text{drop}}{2}\] \[=\frac{1}{2}\times \frac{1}{10}\,cm=\frac{1}{20}\,cm\] Let radius of rim of the glass \[=r\] Hence, height the glass \[=2r\] According to question. \[32000\times \frac{4}{3}\pi \times \frac{1}{20}\times \frac{1}{20}\times \frac{1}{20}\] \[{{r}^{3}}=\frac{32000\times 4}{20\times 20\times 20\times 2}\] \[{{r}^{3}}=8\]\[\Rightarrow \]\[r=2\] \[\therefore \]Height of the glass \[=2r=2\times 2=4\,cm\]


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