SSC Sample Paper SSC CGL - Sample Paper-2

  • question_answer
    A cone of height 9 cm with diameter of its base 18 cm is curved out from a wooden solid sphere of radius 9 cm. The percentage of wood wasted is

    A) \[25%\]%                         

    B)  \[25\pi %\]%

    C)  \[75%\]%

    D)  \[50%\]%

    Correct Answer: C

    Solution :

    \[\therefore \]\[h=9\,cm,\] \[r=9\,cm\] \[\therefore \] Volume of cone \[=\frac{1}{3}\pi {{r}^{2}}h\]             \[=\frac{1}{3}\pi \times 81\times 9=243\pi c{{m}^{2}}\] Volume of solid sphere whose radius is 9 cm             \[=\frac{4}{3}\pi {{(9)}^{3}}\]             \[=\frac{4}{3}\pi \times 9\times 9\times 9=972\pi \,c{{m}^{3}}\] Wastage \[=972\pi -243\pi \]             \[=729\pi \,c{{m}^{3}}\] Percentage of wastage \[=\frac{729\pi }{972\pi }\times 100%\]             \[=75%\]

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