A) 4:3
B) \[\sqrt{6}:\sqrt{\pi }\]
C) \[\sqrt{3}:\sqrt{\pi }\]
D) 22:7
Correct Answer: B
Solution :
[b] \[4\pi \,\,{{r}^{2}}=6{{x}^{2}}\Rightarrow \frac{r}{x}=\sqrt{\frac{3}{2\pi }}\] Required ratio \[=\frac{\frac{4}{3}\pi {{r}^{3}}}{{{x}^{3}}}=\frac{4}{3}\pi {{\left( \frac{r}{x} \right)}^{3}}\] \[=\frac{4}{3}\pi \frac{3\sqrt{3}}{2\pi }\frac{1}{\sqrt{2\pi }}\] \[=\frac{\sqrt{6}}{\sqrt{\pi }}\]
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