Static metrics have been widely studied in mathematical relativity. In this talk, I will discuss a functional inequality involving the static potential of a manifold with boundary possessing a static metric and the extrinsic geometry of the boundary. The main ingredient is a (weighted) Reilly formula obtained recently by Qiu and Xia. I will also discuss a related inequality when the metric is not static. If time allows, I will also give some other applications of Reilly-type formulas. Part of it is joint work with Pengzi Miao.