Course: Calculus II
Topic: Geometry
Subtopic: Volume by Shell Method


When finding the volume of a solid of revolution, some solids lend themselves nicely to the slicing methods covered in the previous lesson. Others are better suited for a second method for finding volume called the shell method. This method finds the volume of nested cylindrical shells then uses integration to sum them for the total area of the solid.


By the end of this topic you should know and be prepared to be tested on:


Terms you should be able to define: cylindrical shell, nested cylinders, shell method

Mini-Lectures and Examples

STUDY: Geometry - Volume by Slicing and Shell Methods

Supplemental Resources (recommended):

Visualizing the shell method can be hard at first. Exploring these demonstrations may help:

Supplemental Resources (optional)

Video: Volume Calculations III (Cylindrical Shells), Selwyn Hollis's Video Calculus

Lesson: Solids of Revolution by Shells, Math is Fun (introductory information/examples)

Lesson: Volume with Cylinders, Paul's Online Notes for Calc I

PDF: Additional Applications, Dale Hoffman's Contemporary Calculus (starting on page 5, "Volumes of Revolution Using Tubes (Shells)")

rev. 2021-01-09