2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137283We define the ``volume'' contained by pointed $k$-surfaces, first studied by the author in [9], and we show that this volume is always finite. Likewise, we show that the surface area of a pointed $k$-surface is always finite.Differential Geometry53C42; 30F60; 51M10; 53C45; 58D10Finite area and volume of pointed $k$-surfacestext