Slicing Solids: Cutting a Sphere with a Moving Plane

This GeoGebra activity demonstrates how a moving plane (controlled by translation/rotation) slices a sphere and how the intersection curve/section evolves as the plane’s position changes. It focuses on solid-geometry concepts such as the intersection of a plane with a sphere, the resulting cross-section geometry, and the idea of relating geometric configurations to corresponding (often piecewise) behavior. Construction-wise, it uses GeoGebra commands including Point (to define key geometric locations), Circle (for auxiliary/cross-section circular elements), Sphere (to model the 3D solid), Intersect (to compute intersection objects), IntersectPath (to handle intersections along constructed paths), and Translate (to move the slicing setup). The model also relies on Vertex to structure key points/objects (A, B, c, C, b, D, E, F, G) and on transformation controls (tilt, turn, shift) to dynamically adjust the slicing plane, while text labels (text1–text3) communicate the key results. Suitable for upper-secondary and introductory college students for classroom demonstrations and exploratory learning in 3D geometry.