Calculating Volumes: Proving Cylindrical Shell Disks

[Miike012]

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?

 

[Dick]

There are tons of them. What did you type into your search engine? http://www.google.com/#hl=en&gs_nf=...or.r_gc.r_pw.r_qf.,cf.osb&fp=7f11edaceb0ef551

 

[Miike012]

I typed in cylindrical shells proof and proof of cylindrical shells...

 

[Miike012]

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.

 

[Dick]

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.