A) 1 : 3
B) 1 : 6
C) 1 : 9
D) 1 : 18
Correct Answer: C
Solution :
Let sides of two cubes be \[{{a}_{1}}\] and \[{{a}_{2}}\] So, \[\frac{a_{1}^{3}}{a_{2}^{3}}=\frac{1}{27}.\] Taking cube root, we get \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{1}{3}\] Area of face of first cube \[=a_{1}^{2}\] And area of face of other cube \[=a_{2}^{2}\] \[\therefore \] Required ratio \[=\frac{a_{1}^{2}}{a_{2}^{2}}={{\left( \frac{{{a}_{1}}}{{{a}_{2}}} \right)}^{2}}\] \[={{\left( \frac{1}{3} \right)}^{2}}=\frac{1}{9}=1:9\]
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