A) \[81:1\]
B) \[9:1\]
C) \[3:1\]
D) \[27:1\]
Correct Answer: A
Solution :
(a): Let the slant height of 1st cone = L Then the slant height of 2nd cone = 3L Let the radius of 1st cone \[={{r}_{1}}\] And let the radius of 2nd cone \[={{r}_{2}}\] Then, \[\pi {{r}_{1}}L=3\times \pi {{r}_{2}}\times 3L\] \[\Rightarrow \] \[\pi {{r}_{1}}L=9\pi {{r}_{2}}L\] \[\Rightarrow \] \[{{r}_{1}}=9{{r}_{2}}\] Ratio of area of the base \[\frac{\pi r_{1}^{2}}{\pi r_{2}^{2}}\] \[\Rightarrow \] \[{{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{2}}={{\left( \frac{9}{1} \right)}^{2}}\] \[\Rightarrow \] \[81:1\]
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