Civil Engineering
Learn the fundamentals of solid mensuration, covering core terminology, regular polyhedra, right vs oblique solids, similar solids, mass/density, and Cavalieri's Principle.
Basic introductory examples covering similar solids and volume proportionality.
Learn about polyhedra, prisms, their formulas for volume and surface area, including regular polyhedra, general prisms, cubes, truncated prisms, and pyramids.
Examples and applications for polyhedra and prisms, including cubes.
Formulas and concepts for cylinders and cones, including volumes, surface areas, truncated cylinders, cylindrical ungula, frustums, and paraboloids of revolution.
Examples and applications for cylinders and cones.
Comprehensive guide to spheres and spherical geometry, including Archimedes' Relationship, spherical segments, wedges, and polygons.
Examples and applications for spheres and spherical geometries.
Advanced solid mensuration concepts including the Theorems of Pappus, ellipsoids, toruses, and volume estimation for irregular shapes using Trapezoidal and Simpson's rules.
Examples and case studies for advanced shapes, irregular volume estimation (earthworks), and the theorems of Pappus.