The small-angle scattering correlation function of a particle gamma(r) results from scattering experiments. This function possesses a well-defined slope gamma'(0) at the origin. This slope is defined by the particle volume V and the whole surface area S of the particle via gamma'(0) = -S/(4V). In this paper it is demonstrated that this slope defines the mean chord length of the particle, (l) over bar = -1/gamma'(0) = 4V/S. This theorem involves non-convex particles, especially the case of particles with hollow parts. Consequently, for a large class of particle shapes the mean chord length is defined in terms of V and S. This extension of the Cauchy theorem is developed by closer analysis of the set covariance C(r), of the small-angle scattering correlation function gamma(r), and of the so-called linear erosion P(r) near the origin r-->0. The cases of a single hollow sphere, of two touching spheres, and of the single hollow cylinder are discussed.