2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/154598Using combinatorial methods, we derive several formulas for the volume of convex bodies obtained by intersecting a unit hypercube with a halfspace, or with a hyperplane of codimension 1, or with a flat defined by two parallel hyperplanes. We also describe some of the history of these problems, dating to Polya's Ph.D. thesis, and we discuss several applications of these formulas.11 pages; minor corrections to referencesMetric GeometryCombinatorics52A38, 52B11 (Primary) 05A19, 60D05 (Secondary)text