Question

The volume of a cube is $V$. What is the total length of its edges?

• A. $6V^{1/3}$
• B. $8\sqrt{V}$
• C. $12V^{2/3}$
• D. $12V^{\frac{1}{3}}$

Answer 1

The correct option is D $12V^{\frac{1}{3}}$

We know, Volume of a cube $=$ $($edge${)}^3$.

Then, $V=$ $($edge${)}^3$.

$\Rightarrow$ edge $=\sqrt[3]{3V}$

$\Rightarrow$ edge $=V^{\frac{1}{3}}$.

Since a cube has $12$ edges,

the total length of its edges $=12\times V^{\frac{1}{3}}=12V^{\frac{1}{3}}$.

Therefore, option $D$ is correct.