A) \[\sqrt{2}:1\]
B) 2 : 1
C) 1 : 2
D) 1 : 4
Correct Answer: A
Solution :
Given that, \[{{V}_{1}}={{V}_{2}}\] and \[{{h}_{1}}:{{h}_{2}}=1:2\] \[\therefore \] \[\pi r_{1}^{2}{{h}_{1}}=\pi r_{2}^{2}{{h}_{2}}\] \[\Rightarrow \] \[{{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{2}}=\frac{{{h}_{2}}}{{{h}_{1}}}=\frac{2}{1}\] \[\Rightarrow \] \[\frac{{{r}_{1}}}{{{r}_{2}}}=\frac{\sqrt{2}}{1}\] \[\Rightarrow \] \[{{r}_{1}}:{{r}_{2}}=\sqrt{2}:1\]
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