A) \[\sqrt{3}:\sqrt{2}\]
B) \[3\sqrt{3}:\sqrt{2}\]
C) \[\sqrt{3}:2\sqrt{2}\]
D) \[\sqrt{2}:\sqrt{6}\]
Correct Answer: B
Solution :
(b): \[\frac{Volume\text{ }of\text{ }cone}{Volume\text{ }of\text{ }cylinder}\] \[=\frac{\pi {{r}_{1}}^{2}{{h}_{1}}}{\pi {{r}_{2}}^{2}{{h}_{2}}}=3.{{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{2}}\left( \frac{{{h}_{1}}}{{{h}_{2}}} \right)\] \[=3\times {{\left( \frac{\sqrt{3}}{\sqrt{2}} \right)}^{2}}\times \frac{\sqrt{2}}{\sqrt{3}}=3\times \frac{\sqrt{3}}{\sqrt{2}}=3\sqrt{3}:\sqrt{2}\]
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