When to use Disk vs Shell vs Washer

  • Thread starter Thread starter duki
  • Start date Start date
  • Tags Tags
    Disk Shell
Click For Summary

Homework Help Overview

The discussion revolves around determining when to use the Shell, Disk, or Washer methods for calculating volumes of solids of revolution in calculus. Participants express uncertainty about the criteria for selecting the appropriate method based on the problem's geometry.

Discussion Character

  • Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the importance of sketching the problem and identifying the cross sections to determine the method. Questions arise about how to decide which method is easiest based on the sketch. There is mention of the potential need to split integrals depending on the chosen method.

Discussion Status

The conversation includes various perspectives on the selection process for the methods. Some participants provide guidance on sketching and visualizing the problem, while others share their experiences of struggling with the decision-making process. There is no explicit consensus, but a sense of exploration and shared learning is evident.

Contextual Notes

Participants note that experience and visual representation play significant roles in determining the method, indicating that there may not be a straightforward rule applicable to all scenarios.

duki
Messages
264
Reaction score
0
Can someone explain to me when you should user the Shell / Disk / Washer methods? I don't understand how to determine which method to use.
 
Physics news on Phys.org
Sketch a picture of the problem. Pick an axis to integrate along that looks like it will be the easiest. Now look at the cross sections of the area along that axis. Are they disks, shells or washers? You can do it more than one way. The picture is the most important part.
 
I often sketch the picture and can't decide which method to use. Is there a way to tell which will be easiest for the given sketch?
 
About the only difference is sometimes one method will require you to split the integral into multiple parts and another won't. There's no method I can describe in words, looking at the picture and experience will tell you.
 
You know how sometimes you think about stuff for like three hours and can't figure it out... but then all of a sudden something just "clicks"?

That just happened... Thanks for your help!
I'm going to wait to mark this as solved to make sure I got it down.
 

Similar threads

Undergrad Can you solve a Disk, Washer, Shell method problem without drawing a graph?
  • · Replies 4 ·
Replies
4
Views
2K
Disk, Washer, Shell Multiple Integrals
  • · Replies 3 ·
Replies
3
Views
4K
Help with Disk/washer and Shell method
  • · Replies 7 ·
Replies
7
Views
5K
Which Method to Use for Finding Volume of Revolved Solid?
  • · Replies 16 ·
Replies
16
Views
3K
How to find the new limits of integration
  • · Replies 1 ·
Replies
1
Views
4K
Washer vs cylindrical shell method for computing volumes
  • · Replies 1 ·
Replies
1
Views
10K
Volumes of Rotating Functions: Shell vs. Washer Method
  • · Replies 2 ·
Replies
2
Views
2K
Integrating by Volume: Calculating Solid Volume Using Disk/Washer Method
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad How to apply the disk/washer and shell methods
  • · Replies 1 ·
Replies
1
Views
2K
What are the methods for finding volume using washers and shells?
  • · Replies 6 ·
Replies
6
Views
3K