Volume of Spheres Copy (no proof window)

① This GeoGebra example demonstrates the volume of a sphere in relation to cylinders and cones through an interactive 3D visualization, allowing learners to intuitively grasp the derivation of the sphere volume formula. ② Core mathematical concepts include sphere volume, cylinder volume, cone volume, inscribed circles, polygonal approximation, solids of revolution, and volume optimization ideas from linear programming. ③ Construction highlights: using GeoGebra commands such as Circle, Point, Sphere, Cylinder, Cone, Segment, OrthogonalPlane, IntersectPath, Intersect, Rotate, Polygon, Sequence, Angle, and Surface, the model builds a sphere, cylinder, cone, and auxiliary cross-sections, with rotation and intersection paths to create multiple solids for dynamic exploration. ④ Suitable for upper secondary or early university students studying solid geometry and volume formulas, and useful for teachers as a classroom demonstration tool, especially for exploring the proportional relationships among sphere, cylinder, and cone volumes.