Change in Volume Per Unit Change in Depth

This GeoGebra example dynamically illustrates how the volume of a cylinder changes as its depth (height) increases, focusing on the incremental volume gained per unit increase in depth. It visually demonstrates the concept of rate of change and derivative, using the linear relationship V = πr²h for a cylinder. The construction employs the Circle command to define the base, Cylinder to generate the solid, Volume to compute the current volume, and Point objects with sliders to control depth, while Texta displays numerical values. This is ideal for high school or introductory college calculus students to grasp the geometric meaning of derivative as an instantaneous rate of change, and to explore the proportional relationship between volume and depth.