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

Click here to go to the next page
