  We argue that in cuprate physics there are two types, hole content per
CuO$_2$ plane ($P_{pl}$) and the corresponding hole content per unit volume
($P_{3D}$), of hole-doping concentrations for addressing physical properties
that are two-dimensional (2D) and three-dimensional (3D) in nature,
respectively. We find that superconducting transition temperature ($T_c$)
varies systematically with $P_{3D}$ as a superconducting \textquotedblleft
$dome$\textquotedblright with a universal optimal hole-doping concentration
$P_{3D}^{opt.}$ = 1.6 $\times$ 10$^{21}$ cm$^{-3}$ for single-layer high
temperature superconductors. We suggest that $P_{3D}^{opt.}$ determines the
upper bound of the electronic energy of underdoped single-layer high-$T_c$
cuprates.
