A) \[\sqrt{2}:\sqrt{3}\]
B) \[\sqrt{3}:1\]
C) \[\sqrt{3}:\sqrt{2}\]
D) \[2:\sqrt{3}\]
Correct Answer: C
Solution :
(c): Let the Radius of hemisphere = Height of cylinder =r units \[\therefore \frac{Volume\text{ }of\text{ }hemisphere}{Volume\text{ }of\text{ }cylinder}=1\] \[\Rightarrow \frac{\frac{2}{3}\pi {{r}^{3}}}{\pi {{r}_{1}}^{2}}=1\Rightarrow \frac{{{r}^{2}}}{{{r}_{1}}^{2}}=\frac{3}{2}\] \[\Rightarrow \frac{r}{{{r}_{1}}}=\frac{\sqrt{3}}{\sqrt{2}}or\sqrt{3}:\sqrt{2}\]
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