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 $2\sqrt{2}V$

Let the length of each edge is $a.$

$S=6a^2$ and $V=a^3$

Now $S=12a^2$

$=6\times 2a^2$

$=6(\sqrt{2}a{)}^2$

$\therefore$ length of each edge $=6(\sqrt{2}a{)}^2$

$Volume=(\sqrt{2}a{)}^3=2\sqrt{2}{a}^3=2\sqrt{2}V$.