A) 2 : 3
B) 4: 9
C) 8: 27
D) 64: 729
Correct Answer: D
Solution :
Let the radii of the first and second spheres be \[{{r}_{1}}\] and \[{{r}_{2}}\] units respectively. According to the question, \[\frac{4\pi r_{1}^{2}}{4\pi r_{2}^{2}}=\frac{4}{9}\] \[\Rightarrow \] \[\frac{r_{1}^{2}}{r_{2}^{2}}=\frac{4}{9}\] \[\Rightarrow \] \[\frac{{{r}_{1}}}{{{r}_{2}}}=\frac{2}{3}\] \[\therefore \] \[\frac{{{V}_{1}}}{{{V}_{2}}}=\frac{\frac{4}{3}r_{1}^{3}}{\frac{4}{3}r_{2}^{3}}=\frac{r_{1}^{3}}{r_{2}^{3}}\] \[={{\left( \frac{2}{3} \right)}^{3}}=\frac{8}{27}\]
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