Answer
$A=\pi \frac{S}{6}$
Work Step by Step
Let $s$ represent a length of a side of the cube and $S$ represent the surface area of the cube.
Let $A$ represent the surface area of the sphere.
Surface area of the sphere is,
$A=4\pi {{r}^{2}}$
Substitute the value $r=\frac{s}{2}$ in the equation.
$\begin{align}
& A=4\pi {{r}^{2}} \\
& =4\pi {{\left( \frac{s}{2} \right)}^{2}} \\
& =4\pi \frac{{{s}^{2}}}{4} \\
& =\pi {{s}^{2}}
\end{align}$
Therefore, the surface area of the sphere is $\pi {{s}^{2}}$.
The surface area of the cube is $S=6{{s}^{2}}$.
Divide both the sides of the equation $S=6{{s}^{2}}$ by 6,
$\begin{align}
& \frac{S}{6}=\frac{6{{s}^{2}}}{6} \\
& \frac{S}{6}={{s}^{2}}
\end{align}$
$\begin{align}
& A=\pi {{s}^{2}} \\
& =\pi \frac{S}{6}
\end{align}$
