Cross-Sections of a Sphere, Cone, and Cylinder: Cutting with a Moving Plane

This example demonstrates how the same cutting process—intersecting a solid with a (typically orthogonal) plane—produces different cross-sectional curves for a sphere, a cone, and a cylinder. It highlights the geometric phenomenon that the cross-section shape depends on the solids’ equations/structure and the plane’s position. Key concepts include solid geometry slicing, cross-section curves (e.g., circles), and construction techniques using orthogonal planes/lines to control the slice. In GeoGebra, it builds the solids with Sphere, Cylinder, and Cone; defines a slicing/orthogonal cutting plane via OrthogonalPlane (and related helpers like OrthogonalLine); computes the intersection curve using IntersectPath; and uses Vector and Translate to specify direction/placement (e.g., for moving the cutting plane). Circle, Point, and Corner help locate and visualize critical geometric elements of the sections. Suitable for middle school through early undergraduate solid geometry lessons, classroom demonstrations, and learners practicing spatial intuition and geometric construction.