Question

If a cube has surface area $S$ and volume $V$, then the volume of the cube of surface area $2S$ is:

• A. $\sqrt{2}V$
• B. $2V$
• C. $2\sqrt{2}V$
• D. $4V$

Answer 1

The correct option is C $2\sqrt{2}V$

Length of each edge $=$ $a$.
Then, Surface area of cube $S=6a^2$
and Volume of the cube $V=a^3$.
Now, new surface area $=$ $2S=2\times 6a^2=12a^2$ = $6\times 2a^2$ = $6\times (\sqrt{2}a{)}^2$.

Then, length of each edge with surface area, $2S$ $=\sqrt{2}a$
Thus, volume $=(\sqrt{2}a{)}^3$ = $2\sqrt{2}{a}^3$ = $2\sqrt{2}V$.

Hence, option $C$ is correct.