Cross Sections of Cone, Sphere, and Cylinder

①This example dynamically demonstrates the shapes and variations of cross sections obtained by cutting a cone, a sphere, and a cylinder with a plane, vividly illustrating the core phenomenon of cross-section problems in solid geometry. ②Core mathematical concepts involved include cross sections of solids, conic sections (circle, ellipse, parabola, hyperbola), great and small circles of a sphere, circular or elliptical sections of a cylinder, and the special role of equilateral triangles in certain sections. ③Construction highlights: Based on the construction summary, GeoGebra commands such as Point, Circle, Distance, Segment, and Intersect are used, creating objects A, f, D, B, E, c, e, d, r₂, r₃, text1, text2, g, C, F, h, i, and text3. The section plane is dynamically adjusted via control points and auxiliary lines, with text objects displaying relevant measurements or explanations. ④This is suitable for high school solid geometry teaching, introductory analytic geometry in university, and math enthusiasts exploring 3D section properties. It can be used for classroom demonstrations or self-directed exploration to enhance spatial visualization skills.