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The volumes of two cubes are in the ratio 8 : 27. The ratio of their surface areas is :
Answer & Solution
Correct Answer:
Option
B
Let their edges be a and b
Then,
$$\eqalign{ & \frac{{{a^3}}}{{{b^3}}} = \frac{8}{{27}} \cr & \Rightarrow {\left( {\frac{a}{b}} \right)^3} = {\left( {\frac{2}{3}} \right)^3} \cr & \Rightarrow \frac{a}{b} = \frac{2}{3} \cr & \Rightarrow \frac{{{a^2}}}{{{b^2}}} = \frac{4}{9} \cr & \Rightarrow \frac{{6{a^2}}}{{6{b^2}}} = \frac{4}{9}\,Or\,4:9 \cr} $$
Then,
$$\eqalign{ & \frac{{{a^3}}}{{{b^3}}} = \frac{8}{{27}} \cr & \Rightarrow {\left( {\frac{a}{b}} \right)^3} = {\left( {\frac{2}{3}} \right)^3} \cr & \Rightarrow \frac{a}{b} = \frac{2}{3} \cr & \Rightarrow \frac{{{a^2}}}{{{b^2}}} = \frac{4}{9} \cr & \Rightarrow \frac{{6{a^2}}}{{6{b^2}}} = \frac{4}{9}\,Or\,4:9 \cr} $$
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