Solid Mensuration

Foundations of solid mensuration covering dimensional reasoning, plane-geometry prerequisites, terminology, units, polyhedra, similarity, Cavalieri, prismatoidal reasoning, Pappus, density, and engineering applications.

Complete treatment of polyhedra and prisms, including Euler's relation, Platonic solids, right and oblique prisms, parallelepipeds, cubes, truncated prisms, and a bridge to pyramids.

Comprehensive solid mensuration treatment of pyramids and cones, including classification, volume, slant height, surface area, similar cross-sections, centroids, and engineering interpretation.

Comprehensive treatment of cylinders and related circular solids, including right and oblique cylinders, pipes, truncated cylinders, cylindrical ungulas, cones, paraboloids, and an introduction to frustums.

Complete treatment of conical and pyramidal frustums, including similarity, direct volume formulas, lateral area, slant height, reconstruction, and engineering capacity applications.

Comprehensive treatment of spheres, spherical shells, caps, zones, segments, sectors, wedges, lunes, spherical polygons, great-circle distance, and Archimedes' relationship.

Complete treatment of similarity in three dimensions, area and volume scale laws, Cavalieri's principle, oblique solids, cross-sections, and engineering scaling applications.

Advanced solid mensuration covering Pappus-Guldinus theorems, ellipsoids, toruses, composite solids, prismatoidal volume, and numerical estimation from parallel sections.