Min Surface Area of Cylinder (fixed volume)

This example demonstrates how to find the minimum surface area of a cylinder under a fixed volume constraint. By analyzing the surface area formula S=2πr(h+r) and using derivatives to find extrema, it reveals the relationship between volume and surface area. Key mathematical concepts include geometric volume calculation, derivative application, and optimization. Construction involves using GeoGebra commands like Cylinder, Locus, and Distance to create the cylinder, establish volume constraints, and compute surface area. Suitable for high school students or college freshmen learning solid geometry and calculus fundamentals.