  In this paper, we will study the limiting behavior of the Brown-York mass of
the coordinate spheres in an asymptotically flat manifold. Limiting behaviors
of volumes of regions related to coordinate spheres are also obtained,
including a discussion on the isoperimetric mass introduced by Huisken
\cite{Huisken}. We will also study expansions of the Brown-York mass and the
Hawking mass of geodesic spheres with center at a fixed point $p$ of a three
manifold. Some geometric consequences will be derived.
