Chapter 10

Pump Up the Volume: Using Calculus to Solve 3-D Problems

In This Chapter

arrow Understanding the meat-slicer method for finding volume

arrow Using inverses to make a problem easier to solve

arrow Solving problems with solids of revolution and surfaces of revolution

arrow Finding the space between two surfaces

arrow Considering the shell method for finding volume

In Chapter 9, I show you a bunch of different ways to use integrals to find area. In this chapter, you add a dimension by discovering how to use integrals to find volumes and surface areas of solids.

First, I show you how to find the volume of a solid by using the meat-slicer method, which is really a 3-D extension of the basic integration tactic you already know from Chapter 1: slicing an area into an infinite number of pieces and adding them up.

As with a real meat slicer, this method works best when the blade is slicing vertically — that is, perpendicular to the x-axis. So I also show you how to use inverses to rotate some solids into the ...

Get Calculus II For Dummies, 2nd Edition now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.