Question

Two cubes have edge lengths in the ratio of 2:3 respectively.
The ratio of the length of the diagonal of a face of the first cube to the length of the diagonal of a face in the second 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 anathor cube be $b$
• We have $\frac{a}{b}=\frac{2}{3}$
• Ratio of lengths of the diagonal of a face of the first cube to the second cube is $\frac{\sqrt{2}a}{\sqrt{2}b}=\frac{a}{b}=\frac{2}{3}$