By a combination of analytical and numerical methods, the density profile of a spherical star momentarily at rest is varied, and the corresponding response in the area of the spherical shells is monitored. It is shown that the inner apparent horizon (if it exists) must lie within or at most on the star's surface while no such restriction is found for the outer apparent horizon. An apparent horizon, however, lying in the vacuum region will always have a nonvanishing area, as long as the ADM mass of the system is nonzero. Furthermore for density profiles not decreasing outwards, it appears that all spherical trapped surfaces lie on a thick spherical shell