Answer:
Given: \[{{P}_{1}}=3{{P}_{2}}\] or \[\frac{4\sigma }{{{r}_{1}}}=\frac{3\times 4\sigma }{{{r}_{2}}}\] or \[{{r}_{2}}=3{{r}_{1}}\] \[\therefore \] \[\frac{{{V}_{1}}}{{{V}_{2}}}=\frac{\frac{4}{3}\pi r_{1}^{3}}{\frac{4}{3}\pi r_{2}^{3}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{3}}={{\left( \frac{1}{3} \right)}^{3}}=\mathbf{1:27}\]
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