A) 27 : 64
B) 3 : 4
C) 9 : 16
D) 3 : 8
Correct Answer: C
Solution :
\[\because \] \[\frac{{{V}_{1}}}{{{V}_{2}}}=\frac{27}{64}\] Let \[{{a}_{1}}\] and \[{{a}_{2}}\] are the sides of two cubes. \[\therefore \] \[\frac{a_{1}^{3}}{a_{2}^{3}}=\frac{27}{64}={{\left( \frac{3}{4} \right)}^{3}}\] \[\Rightarrow \] \[{{a}_{1}}:{{a}_{2}}=3:4\] \[\therefore \] Ratio of their total surface area \[=\frac{6a_{1}^{2}}{6a_{2}^{2}}\] \[={{\left( \frac{{{a}_{1}}}{{{a}_{2}}} \right)}^{2}}={{\left( \frac{3}{4} \right)}^{2}}\] \[=9:16\]
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