Gauss's Law states that
$\begin{align*}\int_{\text{surface}} \mathbf{E} \cdot d \mathbf{A} = \frac{Q_{\text{enclosed}}}{\epsilon_0}\end{align*}$
We are told that $Q_{\text{enclosed}} = 1 \cdot 10^{-9} \mbox {C}$ , so the total flux through the surface is
$\begin{align*}\frac{Q_{\text{enclosed}}}{\epsilon_0} &= \frac{1 \cdot 10^{-9} \mbox { C}}{8.85 \cdot 10^{-12} \;\mathrm{C...$
So, the flux through the rest of the surface is approximately $\boxed{200 \;\mathrm{N}\;\mathrm{m}^2\mathrm{/}\mathrm{C}}$ . Therefore, answer (E) is correct.

Solution to 2008 Problem 62