# 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.