Related Rates: Filling/Draining Cone Dynamic Simulation

This GeoGebra example dynamically demonstrates the related rates problem of filling or draining a conical container, showing how the liquid height, surface radius, and volume change interdependently over time. The core mathematical concepts include related rates in calculus, the volume formula for a cone, similar triangles to relate height and radius, and implicit differentiation. The construction uses GeoGebra commands such as Point, Segment, Polygon, Intersect, Distance, and Slider to build the cone cross-section, compute the liquid surface intersection, and animate the filling/draining process. A Textfield displays real-time values. This resource is suitable for high school seniors or introductory college calculus students, serving as an interactive visual aid for understanding related rates problems and as a tool for classroom demonstration or self-study.