Register to reply 
Shell method VS washer/disk method 
Share this thread: 
#1
Oct3008, 10:53 PM

P: 5

i'm confused right now about this, when would it be appropriate to use the shell method rather than using the washer or disk method when it comes to looking for the volume of a rotating object?



#2
Oct3108, 06:44 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,683

Often either can be used. It really depends upon whether it is easier to write y as a function of x or x as a function of y and whether the axis of rotation is parallel to the x or y axis.
If you have y as a function of x, and the axis of rotation is parallel to the xaxis, then your "disk radius" will depend on y but you will be integrating with respect to x so you will, as you want, be integrating a function of x with respect to x. That would be using the disk method. If you have y as a function of x, and the axis of rotation is parallel to the yaxis, trying to use the disk method, your "disk radius" will depend on x but you want to integrate with respect to y and x is NOT a function of y. That will cause difficulties. Use the shell method here. If you have x as a function of y, reverse the two above. Of course, if you can easily write both y as a function of x and x as a function of y, it doesn't matter. This makes much more sense for a specific problem than as a general rule! 


#3
Nov208, 11:48 AM

Sci Advisor
HW Helper
P: 9,499

washers/discs are more suitable in terms of x,y,z coords, roughly, and shells in terms of polar coords, so yes i would say to use the latter on a problem with rotational symmetry.
i.e. they are both the same method just expressed in different coords. so use whichever one suits the problem, as halls suggests. 


Register to reply 
Related Discussions  
Volume, washer method and shell method  Calculus  5  
The Disk/Washer Method: Axis Of Revolution Question  Calculus & Beyond Homework  1  
Area and Volume (shell and disk method)  Calculus & Beyond Homework  4  
Disk and Shell Method (Ignore my other thread)  Calculus & Beyond Homework  1  
Shell method versus disk method  Calculus & Beyond Homework  1 