3D solid intersection and volume visualization from constructions

This example demonstrates, in 3D space, how intersecting solids (a cube and a sphere) can be used to construct key geometric points/regions and then visualize or obtain volume-related quantities. It centers on solid geometry concepts such as a sphere, cube, and spatial symmetry, along with the general idea of deriving measure information from precise geometric construction. The construction uses GeoGebra commands including Intersect to determine intersection geometry, Point and Segment to create supporting points and edges, PointIn for locating points relative to objects, Cube to generate the cube, Sphere to generate the sphere, and Volume to compute the resulting volume. The scene is organized by cube faces (e.g., faceABDC, faceBDHE, faceABEF, faceACGF, faceCDHG, faceEFGH) and edges (e.g., edgeAB, edgeAC, edgeCD, edgeBD, edgeBE, edgeDH, edgeEH, edgeEF, edgeAF, edgeFG, edgeCG, edgeGH) and combined with labeled points used for the volume computation (e.g., volumec, volumeb and Pointc₁/Pointb₁). Suitable for upper secondary students and introductory university-level geometry, especially for teaching and learning how spatial relationships lead to measurable volume outcomes in an interactive environment.