Calculating Volumes: Proving Cylindrical Shell Disks

  • Thread starter Thread starter Miike012
  • Start date Start date
  • Tags Tags
    Volumes
Click For Summary

Homework Help Overview

The discussion revolves around the concept of proving the volume calculation method using cylindrical shells, a topic within calculus. Participants are seeking rigorous proofs rather than just formulas or explanations of the method.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants express a desire for actual proofs of the cylindrical shells method, questioning the adequacy of existing resources that only provide formulas. There is also a mention of the need for a rigorous mathematical definition of volume to support such proofs.

Discussion Status

The conversation is ongoing, with participants exploring the availability of proofs and the definitions required to substantiate them. Some guidance has been offered regarding the relationship between different volume calculation methods, but no consensus has been reached on the existence of a satisfactory proof.

Contextual Notes

Participants note the challenge of finding rigorous proofs and the potential disconnect between calculus-level understanding and the requirements for formal mathematical definitions of volume.

Miike012
Messages
1,009
Reaction score
0
I am trying to find proofs on the internet of how cylindrical shells disks work but I can't find any. Are there any proofs out there?
 
Physics news on Phys.org
I typed in cylindrical shells proof and proof of cylindrical shells...
 
I would like an actual proof of how it works...
Most of the websites just give formulas and explain how to calculate the volume but that's not a proof.
 
Well, that is a little bit of a problem. You can find proofs that, say the method of cylindrical shells and the method of disks give you the same answer. To PROVE that that is volume you'll need a rigorous mathematical definition of volume. What is it? I'm not sure it would be useful to you at a calculus level.
 

Similar threads

Find volume of this object using integrals
  • · Replies 6 ·
Replies
6
Views
2K
Volume of a Solid using Cylindrical Shells
  • · Replies 6 ·
Replies
6
Views
3K
Volume of revolution, region bounded by two functions
  • · Replies 1 ·
Replies
1
Views
2K
Volume of a sphere with a cylindrical hole
  • · Replies 2 ·
Replies
2
Views
2K
Cylindrical shells to find volume of a torus
  • · Replies 6 ·
Replies
6
Views
6K
Estimating the Volume of a Cylindrical Shell
  • · Replies 1 ·
Replies
1
Views
2K
Sphere-Cylinder Volume: Using Cylindrical Shells Method for Solid Calculation
  • · Replies 6 ·
Replies
6
Views
2K
Washer vs cylindrical shell method for computing volumes
  • · Replies 1 ·
Replies
1
Views
10K
Finding Volume with Rotational Solids: Cylindrical Shell Method
  • · Replies 4 ·
Replies
4
Views
1K
What is the Volume of the Solid Using Cylindrical Shells for y=-e^(-x^2)?
  • · Replies 1 ·
Replies
1
Views
3K