Question

Two cubes have edge lengths in the ratio of $2:3$ respectively.
The ratio of the length of a diagonal of the first cube to the length of the diagonal of one of its faces 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 D $\frac{\sqrt{2}}{\sqrt{3}}$

Let the edge length of first cube be $a$ and the edge length of second cube be $b$
Given, $\frac{a}{b}=\frac{2}{3}$
Ratio of length of diagonal of first cube to the length of diagonal of one of its faces of second cube is $\frac{\sqrt{3}a}{\sqrt{2}b}=\frac{\sqrt{3}}{\sqrt{2}}\times \frac{2}{3}=\frac{\sqrt{2}}{\sqrt{3}}$