Visualizing Volume of Rotation: From Rectangles to Cones and Pyramids

This GeoGebra example dynamically demonstrates how a plane figure (such as a rectangle or a function curve) rotates around an axis to form a solid of revolution, and computes its volume. The core mathematical concepts include definite integrals (volume of revolution formula), geometric transformations (rotation), and the relationship between prisms/pyramids and cylinders/cones. Construction highlights: the Rotate command is used to rotate objects (e.g., rectangles or function graphs) to generate the surface of the solid, the Surface command constructs the 3D surface, the Integral command calculates the definite integral value, and sliders (n), functions (f), parameters (a, b), and text (text1) are used to dynamically update the volume. This is suitable for high school or early college students learning the geometric meaning of volume of revolution in calculus, and for exploring how the volume depends on the base shape (rectangle vs. triangle), as well as comparing volume formulas for pyramids and cones.