When to use Washer, Shell or Disk

  • Thread starter Pseudo Statistic
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In summary, when solving problems involving integrals and volume, you can choose to use either the Washer, Shell, or Disk method. It is important to visualize the solid and determine which method would be easier to integrate. Sometimes, you may need to try both methods to find the most efficient one. With the Shell method, you can think of a tiny segment forming a cylinder parallel to the axis of rotation, while with the Washer method, the segment is rotating perpendicular to the axis of rotation. It is also helpful to practice using both methods to get a feel for which one is preferable in different situations.
  • #1
Pseudo Statistic
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I'm curious, when am I supposed to use Washer, Shell or Disk method when trying to answer questions involving integrals and volume? Is there something specific I should look out for?
I just can't tell the difference.
Any help is appreciated.
Thanks.
 
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  • #2
You can use whichever one you want. You can integrate using any shape. If you're doing the solids of revolution problems, I always thought that the shell method was easier.
 
  • #3
Oh, I thought you weren't able to choose them on your own and each problem reverted to a specific one or something?
 
  • #4
No, its a matter of how you find it easiest to visualize the solid.
 
  • #5
Depending on how the solid is described, you'll sometimes find the shell method easier to integrate than the washer method and vice versa. If you set up the integral one way and you're finding it hard to evaluate, try using the other method. Try doing the same problems using both methods, it's a good way to get a feel for when one is preferable. Of course sometimes either way will be just as easy (or hard).
 
  • #6
Oh good question! I've been wondering the same thing! Disk is usually pretty obvious b/c it's just a volume of solid revolution, usually there's no hole in the center or whatever the situation usually is.

Deciding between washer or shell can be tricky, and as posted above a lot of the time either method will work, but one might be easier. We actually had a homework assignment on the washer method, then the next homework assignment was to redo all the problems using the shell method! Talk about getting confused!

Some things to keep in mind is when using the shell method, you can think of a tiny segment rotating parallel to the axis of rotation (forming a cylinder). This integral takes the form of: integral(circumference*height*delta r).

When using washer, the segment is rotating perpendicular to the axis of rotation. This yields the integral where you have integral [(pi R^2)-(pi r^2)], where R is the radius of the larger disk or washer, and little r is (you guessed it!) the radius of the smaller or inner disk.

Happy integrating!
 

1. When should I use a washer in my experiment?

Washers are typically used to evenly distribute pressure and prevent damage to the material being fastened.

2. What is the purpose of a shell in scientific experiments?

Shells are commonly used to contain and protect delicate or hazardous materials, such as acids or chemicals.

3. When is it appropriate to use a disk in my research?

Disks are often used as a barrier or spacer between two surfaces, or to evenly distribute forces.

4. Can I substitute a washer for a shell or disk in my experiment?

It is not recommended to substitute one type of fastening component for another, as each serves a specific purpose and may affect the outcome of the experiment.

5. How do I determine which type of fastener to use?

The decision to use a washer, shell, or disk should be based on the specific needs of your experiment and the desired outcome. Consider the materials being used, the forces involved, and any potential hazards before selecting a fastener.

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