  In this work, we consider static manifolds $M$ with nonempty boundary
$\partial M$. In this case, we suppose that the potential $V$ also satisfies an
overdetermined Robin type condition on $\partial M$. We prove a rigidity
theorem for the Euclidean closed unit ball $B^3$ in $\mathbb{R}^3$. More
precisely, we give a sharp upper bound for the area of the zero set
$\Sigma=V^{-1}(0)$ of the potential $V$, when $\Sigma$ is connected and
intersects $\partial M$. We also consider the case where $\Sigma=V^{-1}(0)$
does not intersect $\partial M$.
