How to Find the Volume of a Circular Shape with the StackofPancakes Method of Integration
Geometry tells you how to figure the volumes of simple solids. Integration enables you to calculate the volumes of an endless variety of much more complicated shapes. The stackofpancakes technique works when the crosssections of the 3D shape in question are all circles.
Here’s how it works. Find the volume of the solid — between x = 2 and x = 3 — generated by rotating the curve
about the xaxis.

Determine the area of any old cross section or representative pancake.

Tack on a dx to get the volume of an infinitely thin representative pancake.

Add up the volumes of the pancakes from 2 to 3 by integrating.
Just add some maple syrup and dig in!