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We consider static black holes in Einstein gravity and study parameterscharacterizing 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 asequence 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 inliterature. The Schwarzschild black hole saturates all the inequalities, makingit the biggest of all for given mass. The inequalities include an upper boundof entropy for any quantum system with given energy. We also point out thatsome black holes satisfying the dominant energy condition can trap photons toform a stable photon shield outside the event horizon, but the shadow hides itfrom an observer at infinity.

On the Size of a Black Hole: The Schwarzschild is the Biggest