We present results of simulations of flexible polymers in a sphere that show a steady reduction in the chain dimension with concentration. The 3D confinement leads to a 40% shrinking of the chain size at the overlap concentration φ*. The chain squeezing is intensified by polymer depletion inside a sphere evaluated by a novel formula. The depletion induces the accumulation of polymers in the cavity center. Because this effect is ignored in scaling theory, its predictions are not fully consistent with the simulation results. We provide the validation arguments that the shrinking of coils packed at the threshold φ* in bulk solution is comparable to the squeezing of polymers in a cavity. The size contraction by about 10% at φ* in ring polymers in bulk lies midway between those for the linear polymers in bulk and confined polymers, in harmony with the free-energy penalty for penetration of surrounding restraints.