  We consider static black holes in Einstein gravity and study parameters
characterizing the black hole size, namely the radii of the horizon $R_+$,
photon sphere $R_{\rm ph}$ and black hole shadow $R_{\rm sh}$. We find a
sequence of inequalities $\frac32 R_+\, \le\, R_{\rm ph}\, \le
\,\frac{1}{\sqrt3} R_{\rm sh}\,\le\, 3 M$, where $M$ is the black hole mass.
These are consistent with and beyond the previously known upper bounds in
literature. The Schwarzschild black hole saturates all the inequalities, making
it the biggest of all for given mass. The inequalities include an upper bound
of entropy for any quantum system with given energy. We also point out that
some black holes satisfying the dominant energy condition can trap photons to
form a stable photon shield outside the event horizon, but the shadow hides it
from an observer at infinity.
