A) \[\sqrt{2}:\sqrt{3}\]
B) \[\sqrt{6}:\sqrt{\pi }\]
C) \[4:\pi \]
D) None of these
Correct Answer: B
Solution :
Let the radius of sphere be r and the edge of the cube = x \[\therefore \] By given case surface area are equal. So,\[4\pi {{r}^{2}}=6{{x}^{2}}\] \[\therefore \]\[\frac{r}{x}=\sqrt{\frac{3}{2\pi }}\] \[\therefore \]\[\frac{\text{Volume}\,\,\text{of}\,\,\text{Sphere}}{\text{Volume}\,\,\text{of}\,\,\text{Cone}}=\frac{\frac{4}{3}\pi \,\,{{r}^{3}}}{{{x}^{3}}}=\frac{4}{3}\pi {{\left( \frac{r}{x} \right)}^{3}}\] \[=\frac{4}{3}\pi \frac{3}{2\pi }\cdot \frac{\sqrt{3}}{\sqrt{2}\pi }\] \[=\frac{\sqrt{2}\sqrt{3}}{\sqrt{\pi }}=\frac{\sqrt{6}}{\sqrt{\pi }}\]
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