We can find the volumes of solids of revolution at least in two ways. We have seen a method that slices up the volume into an infinite amount of washers that added together gives the initial volume. Summing this infinite amount of slices leads to an integral. This is called the washer method. We can also decompose the volume into nested cylindrical shells. Summing up an infinite amount of shells also lead to an integral that is equal to the volume of the solid. This method is the one that we will now see and it is called the method of cylindrical shells.
Basic Learning Objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at our next class meeting. Important new vocabulary words are indicated in italics.
- Use the method of cylindrical shells to find volumes of simple solids of revolution, created by rotating simple regions about one of the two axes.
Advanced Learning Objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:
Use the method of cylindrical shells in various contexts.
Decide whether the method of cylindrical shells or the method of washers is more appropriate to compute the volume of a solid of revolution.
To prepare for class
Watch the following video which introduces the method of cylindrical shells.
Do the Preview Activity for this section (on WeBWorK if required by your teacher).
Watch the following video which shows how the sphere can be decomposed into cylindrical shells (first part) or discs (second part).
Watch the last part (starting at 4:54) of this video (you already watched the first part for the previous class):