Subject:
Calculus
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Tags:
Cac077, Shell Method, Solids of Revolution, Washer Method
License:
Creative Commons Attribution Non-Commercial
Language:
English
Media Formats:
eBook, Interactive

Education Standards (1)

Solids of revolution modules

Overview

After completing this section, students should be able to do the following.

  • Understand what a solid of revolution is and the two ways to generate one.
  • Use the procedure of “Slice, Approximate, Integrate” to derive the washer method formula.
  • Use the procedure of “Slice, Approximate, Integrate” to derive the shell method formula.
  • Set up an integral or sum of integrals using the washer method.
  • Set up an integral or sum of integrals using the shell method.
  • Compute volumes using the washer method.
  • Compute volumes using the shell method.
  • Determine whether to use washer or shell method given the variable of integration.
  • Determine the variable of integration given the method.
  • Determine if washer method or shell method is more convenient to set up a volume.

What is a solid of revolution?

Ximera Module

We define a solid of revolution and discuss how to find the volume of one in two different ways.

The washer method

Ximera Module

We use the procedure of ``Slice, Approximate, Integrate" to develop the washer method to compute volumes of solids of revolution.

The shell method

Ximera Module

We use the procedure of ``Slice, Approximate, Integrate" to develop the shell method to compute volumes of solids of revolution.

Comparing washer and shell method

Ximera Module

We compare and contrast the washer and shell method.