I am currently self-teaching myself some calculus stuff and I am a bit confused about all these methods to find the volumes given a function rotated along the $y$- or $x$-axis? So far I have come across so many videos with different method names which is what confuses me.

Is the Ring Method = Washer = Disc method? I know there is also the shell method, but other than that are there only two methods to finding the volume?

  • $\begingroup$ There are two basic methods. Here's an exercise for you: take the disk of unit radius centered at $(1,1)$, and rotate it against whichever axis you like. What are the volume and surface area of the figure thus obtained ? $\endgroup$ – Lucian Feb 7 '15 at 7:36
  • $\begingroup$ A washer is just a disk with a concentric hole. It's basically the same method. $\endgroup$ – David K Mar 9 '15 at 5:48

Each method ought to provide you with the same answer, but each is different. The disk method uses disks to fit the volume of the bounds that you've been given. The Washer Method uses washer-shaped shapes within the solid to establish volume. Last, the Shell Method uses a bushing-shaped representation to establish area. For a more in depth view, I recommend that you visit Khan Academy's progression of videos.


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