Question

If $l$ is the length of a diagonal of a cube of volume $V$, then

• A. $3V=l^3$
• B. $\sqrt{3}V=l^3$
• C. $3\sqrt{3}V=2l^3$
• D. $3\sqrt{3}V=l^3$

Answer 1

The correct option is D

$3\sqrt{3}V=l^3$

Volume of the cube = V

and length of diagonal = l

$\therefore Side=\frac{l}{\sqrt{3}}(\because l=\sqrt{3}a)$

$Volume=(Side{)}^3={\left(\frac{l}{\sqrt{3}}\right)}^3$

$\Rightarrow V=\frac{l^3}{3\sqrt{3}}\Rightarrow 3\sqrt{3}V=l^3$