Sphere Volume Exploration I

① This GeoGebra example dynamically demonstrates the derivation of the volume of a sphere, visually showing the relationship between a sphere and related solids such as cylinders or cones. ② Core mathematical concepts include the sphere volume formula, integration ideas, cross-section methods in solid geometry, and the interplay of functions and optimization problems. ③ Construction highlights: using the IntersectPath command to create circular cross-sections of the sphere with planes, defining key points and segments via Point, Segment, and Intersect, and employing functions f, g, h to control dynamic parameters, with text1 and text2 displaying volume values or formulas. ④ Suitable for high school or early college students to grasp the origin of the sphere volume formula, and as a visual aid for introductory calculus (volumes of revolution).