Mr. Integral
Math notes/Calculus II/Geometry and Physical Applications

Volumes of Revolution — Cheat sheet

CHEAT SHEET   ·   FREE

Choose “Save as PDF” in the print dialog.
On this page

Core rule

Washers: V=π∫(R2−r2)V=\pi\int(R^2-r^2). Shells: V=2π∫(radius)(height)V=2\pi\int(\text{radius})(\text{height}).

Watch for

Measure radii from the actual axis. Match the slice variable to the bounds and avoid overlapping shells.