Volume of Sphere Compared to Volume of Hemisphere

①This GeoGebra example dynamically compares the volume of a sphere with that of a hemisphere, demonstrating that the sphere's volume is exactly twice the hemisphere's volume. ②Core mathematical concepts include solid geometry, sphere and hemisphere volumes, radius, and volume formulas, with visualizations using 2D projections of 3D shapes. ③Construction details: The construction uses commands such as Segment, Circle, Intersect, Point, and Ellipse, and defines objects including A, B, C, h, D, e, f, E, F, b, r, G, g, K, Hemisphere, M, k, N, radius, text1, text2, volume, volume2, text3, text5, text4, text6, H, I, and pic1. These include radius r, volume variables volume and volume2, and text labels for annotations. Sliders or parameters allow dynamic adjustment of the radius to observe volume changes. ④This is suitable for high school or early college students, for teaching solid geometry, verifying volume formulas, or as a reference for teachers creating interactive lessons.