Subject:
Calculus
Material Type:
Module
Provider:
Ohio Open Ed Collaborative
Tags:
Cac077, Shell Method, Solids of Revolution, Washer Method
Language:
English
Media Formats:
eBook, Interactive

# 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.