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

    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.