AP CALCULUS AB/BC
Volumes of Solids of Revolution
Calculate volumes of three-dimensional solids formed by rotating regions around axes using disk, washer, and shell methods. Visualize the disk method V = π∫[a to b] [R(x)]²dx for solids without holes, the washer method V = π∫[a to b] ([R(x)]² - [r(x)]²)dx for solids with holes, and the shell method V = 2π∫[a to b] x·h(x)dx for rotation around vertical axes. Master choosing the most efficient method for each problem.
AP CALCULUS AB/BC
Solid of Revolution 3D Visualizer
Interactive Calculus visualizer converting 2D function areas into 3D volumes of revolution using Disk and Washer methods.