A) \[2:3\]
B) \[4:5\]
C) \[5:6\]
D) \[4:7\]
Correct Answer: A
Solution :
Let radius of two spheres be \[{{r}_{1}}\] and \[{{r}_{2}}\] respectively. Given, ratio of volumes \[=8:27\] \[\Rightarrow \] \[\frac{\frac{4}{3}\pi r_{1}^{3}}{\frac{4}{3}\pi r_{2}^{3}}=\frac{8}{27}\Rightarrow {{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{3}}=\frac{8}{27}\] \[\Rightarrow \] \[\frac{{{r}_{1}}}{{{r}_{2}}}=\frac{2}{3}\,\,\,\,\Rightarrow \,\,\,\,{{r}_{1}}:{{r}_{2}}=2:3\]
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