4. $(10\%)$ Let $\Omega$ be a region (on the $xy$-plane) enclosed by $x=\sqrt{\ln y}$, $x=0$ and $y=e$. Let $S$ be the solid obtained by revolving $\Omega$ about the $y$-axis. Let $V$ be the volume of $S$. $V=\underline{\quad(6)\quad}$.