### If a cube has surface area $S$ and volume $V$, then find the volume of the cube of surface area $3S$.

$3 \sqrt{ 3 }V$

Step by Step Explanation:
1. Let the edge of the cube be $a$. Then,
Surface area, $S = 6a^2$, and
Volume, $V = a^3$.
2. We can say that $a = \left(\dfrac{ S } {6} \right)^{ 1 \over 2 }$. Now let us put this value of $a$ in the expression for volume. $V$ then becomes:
$\left(\dfrac{ S } {6}\right)^{ 3\over 2 }$.
3. Thus, for another cube with surface area $3S$, the volume will be:
\begin{align} &\left(\dfrac{ 3S } {6}\right)^{ 3 \over 2 } \\ = & ( 3 )^{ 3 \over 2 } \times \left(\dfrac{ S } {6}\right)^{ 3\over 2 } \\ = & ( 3 )^{ 3 \over 2 }V \\ = & 3 \sqrt{ 3 }V \end{align}
4. Hence the volume of the other cube is $3 \sqrt{ 3 }V$.