Solid Mensuration Simulations
A collection of interactive 3D visualizations and simulations to help you master concepts in solid mensuration.
Introduction to Solid Mensuration - Theory & Concepts
Learn the fundamentals of solid mensuration, covering core terminology, regular polyhedra, right vs oblique solids, similar solids, mass/density, and Cavalieri's Principle.
Parameters
Polyhedra and Prisms - Theory & Concepts
Learn about polyhedra, prisms, their formulas for volume and surface area, including regular polyhedra, general prisms, cubes, truncated prisms, and pyramids.
Platonic Solids
Euler's Formula Properties
Cylinders and Cones - Theory & Concepts
Formulas and concepts for cylinders and cones, including volumes, surface areas, truncated cylinders, cylindrical ungula, frustums, and paraboloids of revolution.
Cone vs Cylinder Volume Ratio
A cone has exactly one-third the volume of a circumscribing cylinder with the same base radius and height.
Spheres and Spherical Geometry - Theory & Concepts
Comprehensive guide to spheres and spherical geometry, including Archimedes' Relationship, spherical segments, wedges, and polygons.
Archimedes' Relationship
The volume of a sphere inscribed in a cylinder is exactly 2/3 the volume of the cylinder. A cone inscribed in the same cylinder has exactly 1/3 the volume.Ratio = 1 : 2 : 3
Height = 2r = 6.0
Theorems of Pappus and Advanced Shapes - Theory & Concepts
Advanced solid mensuration concepts including the Theorems of Pappus, ellipsoids, toruses, and volume estimation for irregular shapes using Trapezoidal and Simpson's rules.
Torus (Theorems of Pappus)
A torus is generated by revolving a circle about a non-intersecting axis. The volume and surface area are calculated using Pappus's Theorems.
Distance from center of hole to center of tube.
Radius of the tube (generating circle).