Dynamic Lateral Surface Development of a Cone

This GeoGebra applet dynamically demonstrates the geometric process of unfolding a cone's lateral surface into a sector. Through constructions involving rotation, orthogonal planes, and cross-sections, it illustrates how a three-dimensional cone is cut along its slant height and flattened into a two-dimensional sector. Key concepts include the equivalence between the cone's base circumference and the sector's arc length, the correspondence between the slant height and the sector's radius, and the calculation of the sector's central angle. The applet allows users to manipulate the cone's dimensions interactively, observing in real time how changes to the base radius or height affect the resulting sector's properties. This interactive visualization helps students bridge the gap between solid geometry and plane geometry, providing a clear geometric intuition behind the lateral surface area formula of a cone. It is particularly suited for review and practice in solid geometry, helping learners understand the transformation between spatial figures and planar figures.