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