Cylinder Cross-Section from Middle of the Base

This GeoGebra example demonstrates the cross-section of a cylinder when cut by a plane passing through the middle of its base, and further shows how to compute the area of this cross-section using integration. The core mathematical concepts involve solid geometry (cylinder, plane slicing, conic sections) and calculus (definite integrals for area calculation). The construction uses GeoGebra commands such as Segment, Plane, Integral, Text, and Cylinder. Key objects include points (theta, R, B, α, A), planes (PlaneRef, PlaneRef2), functions (f, g, IntFun, IntFun_{Sliced}), and 2D projections (A_{2D}, B_{2D}) to visualize the section in a plane. The example is suitable for high school or early college students to explore the interplay between 3D geometry and integration, and to dynamically observe how the cross-section shape and area change with the cutting plane's position.