  A surface $F$ in a 3-manifold $M$ is called cylindrical if $M$ cut open along
$F$ admits an essential annulus $A$. If, in addition, $(A, \partial A)$ is
embedded in $(M, F)$, then we say that $F$ is strongly cylindrical. Let $M$ be
a connected 3-manifold that admits a triangulation using $t$ tetrahedra and $F$
a two-sided connected essential closed surface of genus $g(F)$. We show that if
$g(F)$ is at least $38 t$, then $F$ is strongly cylindrical. As a corollary, we
give an alternative proof of the assertion that every closed hyperbolic
3-manifold admits only finitely many fibrations over the circle with connected
fiber whose translation distance is not one, which was originally proved by
Saul Schleimer.
