Cross-Section of Two Intersecting Cylinders with Volume/Integral View

This GeoGebra example visualizes the solid cross-section formed by the intersection of two cylinders, highlighting how such a “cut body” can be studied geometrically and then approached with an integral viewpoint. It centers on solid geometry of cylinder-cylinder intersection, the idea of cross-sectional area leading to definite integrals for volume (Bestimmtes Integral), and related optimization/extremal thinking when parameters vary. Construction-wise, it uses GeoGebra commands such as Surface and CurveCartesian to generate parametric surfaces and Cartesian curves. Key objects (r, z1, z2, s1, s2) serve as parameters for radii and slicing/height variables, while Text1–Text3 provide on-figure labels to emphasize the quantities being analyzed. Suitable for high school to early university levels covering solid geometry, coordinate geometry modeling, and calculus-based volume reasoning.