Question

Two cubes have edge lengths in the ratio of $2:3$ respectively. The ratio of their surface areas is

• A. $\frac{4}{9}$
• B. $\frac{8}{27}$
• C. $\frac{2}{3}$
• D. $\frac{\sqrt{2}}{\sqrt{3}}$
• E. $\frac{\sqrt{3}}{\sqrt{2}}$

Answer 1

Answer: (A)

$\frac{4}{9}$

Surface area of cube is $6a^2$, If $a$ is edge length
Let the edge length of one cube be $a$ and the edge length of another cube be $b$

Given $\frac{a}{b}=\frac{2}{3}$
Ratio of surface areas is $\frac{6a^2}{6b^2}={\left(\frac{a}{b}\right)}^2={\left(\frac{2}{3}\right)}^2=\frac{4}{9}$