A) \[\sqrt{3}\pi :2\]
B) \[2:\sqrt{3}\pi \]
C) \[3:\sqrt{2}\pi \]
D) None of these
Correct Answer: B
Solution :
We know that, Diagonal of cube = Diameter of sphere i.e., \[a\sqrt{3}=2\,r\] \[\Rightarrow \] \[a=\frac{2}{\sqrt{3}}\cdot r\] \[\therefore \] Required volume ratio \[=\,\frac{Volume\,of\,cube}{Volume\,of\,sphere}\] \[=\frac{{{(side)}^{3}}}{\frac{4}{3}\pi \,{{r}^{3}}}=\frac{(2r/\sqrt{3})}{\left( \frac{4}{3}\pi {{r}^{3}} \right)}\] \[=\frac{8\times 3}{4\times 3\sqrt{3\pi }}=2:\sqrt{3}\pi \]
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