Question

Two cubes have edge lengths in the ratio of $2:3$, respectively. The ratio of their volumes 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 B $\frac{8}{27}$

We know, Volume of cube is $V=a^3$ , where $a$ is the edge of the cube.
Let the edge length of one cube be $a$ and the edge length of another cube be $b$.

Given, $a:b=2:3$.

Then, Ratio of volumes is $\frac{a^3}{b^3}={\left(\frac{a}{b}\right)}^3={\left(\frac{2}{3}\right)}^3=\frac{8}{27}=8:27$.

Therefore, option $B$ is correct.