Communications of the
Korean Mathematical Society CKMS

We defined and studied a naturally extended hyperbolic space (see \cite{C} and \cite{CK}). In this study, we describe Sforza's formula \cite{sf} and Santal\'o's formula \cite{S}, which were rediscovered and later discussed by many mathematicians (Milnor \cite{M}, Su\'arez-Peir\'o \cite{E}, J. Murakami and Ushijima \cite{J}, and Mednykh \cite{Me}) in the spherical space in an elementary way. Thereafter, using the extended hyperbolic space, we apply the same method to prove their results in the hyperbolic space.

Keywords: hyperbolic space, spherical space, polyhedron, volume