The volumes of two cubes are in the ratio 8 : 27. The ratio of their surface areas is :

Answer: Option B

Let their edges be a and b
Then,
$$\begin{array}{rl}& \frac{a^3}{b^3}=\frac{8}{27}\\ & \Rightarrow {\left(\frac{a}{b}\right)}^3={\left(\frac{2}{3}\right)}^3\\ & \Rightarrow \frac{a}{b}=\frac{2}{3}\\ & \Rightarrow \frac{a^2}{b^2}=\frac{4}{9}\\ & \Rightarrow \frac{6a^2}{6b^2}=\frac{4}{9}Or4:9\end{array}$$