Chapter 8: Volume

In preceding chapters, you calculated volumes in a variety of flag problems. Now you will rotate curves about both horizontal and verticals lines to create solids of revolution. By slicing the solid or by embedding shells, you will learn how to calculate the volume of the solid. You will also learn how to slice other solids to make cross-sections of similar shapes. By accumulating these cross-sections, you can determine the volume of the solid. Finally, you will learn how to determine the length of an arc.

Chapter Goals

Use the disk and washer
methods to calculate the
volume of a solid of revolution.

Use cylindrical shells to
calculate volume.

Use cross-sections to calculate
volumes of solids.

Determine the length of an arc.

Chapter Outline

Section 8.1

You will graph functions and rotate them to form solids of revolution. By slicing a solid to form disks or washers, you will be able to calculate the volume of each slice. Accumulating the volumes of the slices is used to determine volume of the solid.

Section 8.2

You will embed cylindrical shells into your solid of revolution. By calculating the volume of each shell and accumulating those volumes, you will determine the volume of the solid.

Section 8.3

You will cut cross-sections, generating similar slices, for other types of solids. You will produce a model of this and calculate its volume.

Section 8.4

You will develop a method to calculate the arc length of a curve.