Lesson #112
Volumes of Solids of Revolution (Shell Method)

Quote of the Day:

"God is a child; and when he began to play, he cultivated mathematics. It is the most godly of man's games." -- V. Erath

---

Objectives:

The student will compute the volume of solids of revolution using the washer method (slicing with a hole in it), the disk method, and the shell method.

The student will compute the volume of solids of revolution rotated about a line other than the x- or y-axis.

1. Collect homework.

2. Shell Method

Use the Shell Method if

(1) you have a function in terms of x and rotation is around the y-axis or

(2) you have a function in terms of y and rotation is around the x-axis.



Find the volume of one shell and then add them up.

To find the volume of a cylindrical shell, take the circumference of the circle, multiply it by the height to get the lateral surface area, then multiply by the thickness. Then create a Riemann sum and take the limit.



3. To help see the shell method -

(a) Bring in Russian stacking dolls (Use the lower half of the dolls - they look like shells).







(b) Use megaphones

(c) Use margarine tubs

(d) use cup-cake wrappers

4. Example:



5. Example:



6. Distribute Quiz on Volumes of Solids of Revolution

7. Assignment:
Finish p. 456 (2, 5, 11, 22, 25, 35, 36)

Click here to go to the next page

Send any comments or questions to: David Pleacher