  In this paper we obtain an analogue of Toponogov theorem in dimension 3 for
compact manifolds $M^3$ with nonnegative Ricci curvature and strictly convex
boundary $\partial M$. Here we obtain a sharp upper bound for the length
$L(\partial\Sigma)$ of the boundary $\partial\Sigma$ of a free boundary minimal
surface $\Sigma^2$ in $M^3$ in terms of the genus of $\Sigma$ and the number of
connected components of $\partial\Sigma$, assuming $\Sigma$ has index one.
After, under a natural hypothesis on the geometry of $M$ along $\partial M$, we
prove that if $L(\partial\Sigma)$ saturates the respective upper bound, then
$M^3$ is isometric to the Euclidean 3-ball and $\Sigma^2$ is isometric to the
Euclidean disk. In particular, we get a sharp upper bound for the area of
$\Sigma$, when $M^3$ is a strictly convex body in $\mathbb R^3$, which is
saturated only on the Euclidean 3-balls (by the Euclidean disks). We also
consider similar results for stationary stable surfaces.
