Pump Up the Volume: Using Calculus to Solve 3-D Problems
In This Chapter
Understanding the meat-slicer method for finding volume
Using inverses to make a problem easier to solve
Solving problems with solids of revolution and surfaces of revolution
Finding the space between two surfaces
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 ...