  We apply the Riemannian Penrose inequality and the Riemannian positive mass
theorem to derive inequalities on the boundary of a class of compact Riemannian
$3$-manifolds with nonnegative scalar curvature. The boundary of such a
manifold has a CMC component, i.e. a $2$-sphere with positive constant mean
curvature; and the rest of the boundary, if nonempty, consists of closed
minimal surfaces. A key step in our proof is the construction of a collar
extension that is inspired by the method of Mantoulidis-Schoen \cite{M-S}.
