Question

Two cubes have edge lengths in the ratio of 2:3 respectively.
The ratio of the sum of the lengths of the edges of the smaller to the sum of the lengths of the edges of the larger 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

The correct option is C $\frac{2}{3}$

• Let the edge length of one cube be $a$ and the edge length of another cube be $b$ , Given $a/b=2/3$
  
• Ratio of sum of lengths of edges of smaller to sum of lengths of edges of larger is $\frac{12a}{12b}=\frac{a}{b}=\frac{2}{3}$