Volumes of Prisms and Cylinders: From Construction to 3D Modeling

This example demonstrates how to construct prisms and cylinders in GeoGebra and visualize the geometric setup behind their volume relationships. It centers on solid-geometry ideas such as the volume of a prism/cylinder, identifying relevant elements (base and height), and using orthogonality/line direction to establish the correct spatial configuration for volume modeling. The construction uses GeoGebra commands including Point and Segment to define key points and edges, Circle and Intersect to build circular base features and their intersection points, Cylinder to generate the 3D cylinder solid, OrthogonalLine to create perpendicular (height/normal) directions, and Vector together with Ray/Segment for orientation and auxiliary constructions. Named objects (e.g., A–H and others) and text labels (text1) support the step-by-step build from planar geometry to 3D solids. Suitable for middle/high school geometry instruction, review of volume formulas, and classroom demonstrations of geometric construction and spatial reasoning.