Rotating a Circle to Form a Sphere: 3D Geometry in GeoGebra

① This example demonstrates how rotating a circle around an axis generates a three-dimensional sphere, visualizing the transition from a 2D shape to a 3D solid. ② Core mathematical concepts include rotation of a circle, sphere formation, parametric surface equations in 3D space, and the relationship between volume and surface area of a solid of revolution. ③ Construction highlights: Using GeoGebra's Surface command with objects f (circle), n (rotation axis), a (angle parameter), and g (auxiliary solid), the sphere is built via a parametric surface, possibly incorporating line segments, rectangles, or other helpers to clarify the process. ④ Suitable for high school or early college students learning solid geometry, spatial reasoning, and parametric surfaces, as well as for teachers demonstrating the generation of solids of revolution in class.