Solid with Circular Base and Square Vertical Cross-Section

This applet constructs a three-dimensional solid whose base is a circle lying in the horizontal plane and whose vertical cross-sections perpendicular to the base are squares. The model is built using GeoGebra's Surface command to generate the curved lateral faces and the Prism command to create the square cross-sectional slices at various positions along the base. By manipulating the parameters, users can observe how the square cross-sections vary in size depending on their distance from the center of the circular base, with the largest square occurring at the diameter and the square shrinking to a point at the edges of the circle. The applet serves as a powerful visual aid for two major areas of mathematics. In solid geometry, it helps students understand how a solid can be defined by specifying the shape and size of its cross-sections at every level. Students can rotate the model in 3D view, toggle individual cross-sections on or off, and dynamically adjust the radius of the base circle to explore how these changes affect the overall shape of the solid. In calculus, the applet directly supports the method of slicing for computing volumes. The square cross-sectional area at any position x along the base can be expressed as a function of x, and students can visually connect this area function to the definite integral that gives the total volume of the solid. By animating the cross-sections or highlighting specific slices, learners gain an intuitive grasp of how integration accumulates infinitesimal area elements to produce a volume. This concrete visualization bridges the gap between abstract integral formulas and their geometric meaning, making it particularly valuable for students encountering volume by slicing for the first time. Overall, this interactive model combines dynamic geometry construction with conceptual clarity, offering an engaging hands-on tool for both high school geometry courses and introductory college calculus classes.