  We discuss the spatial limit of the quasi-local mass for certain ellipsoids
in an asymptotically flat static spherically symmetric spacetime. These
ellipsoids are not nearly round but they are of interest as an admissible
parametrized foliation defining the Arnowitt-Deser-Misner (ADM) mass. The
Hawking mass of this family of ellipsoids tends to $-\infty$. In contrast, we
show that the Hayward mass converges to a finite value. Moreover, a positive
mass type theorem is established. The limit of the mass has a uniform positive
lower bound no matter how oblate these ellipsoids are. This result could be
extended for asymptotically Schwarzschild manifolds. And numerical simulation
in the Schwarzschild spacetime illustrates that the Hayward mass is
monotonically increasing near infinity.
