Maximum Volume of a Cylinder Cut from a Sphere

This example demonstrates how to cut a cylinder from a sphere and find its maximum volume. Key mathematical concepts include volume calculation in solid geometry and optimization problems. Using GeoGebra commands such as Intersect, Vector, and SurdText, the intersection between the cylinder and sphere is visually demonstrated, and the height and base radius of the cylinder can be dynamically adjusted to explore volume changes. Suitable for high school mathematics education and learning optimization problems in solid geometry.