For some reason, in calculus classes here in the U.S. we spend a lot of time teaching students how to find the volume of solids of revolution. This is invariably confusing, because often students try to memorize the various "methods" (disk, washer, cylindrical shell) and have trouble getting a handle on the actual geometry. When I've taught this, I've encouraged my students to draw lots of pictures. This is more than I can say for some textbooks, which try to give "rules" of the form "if a curve is entirely above the x-axis, and it's being rotated around the x-axis, between y = a and y = b, then here's the formula" -- I don't recall explicitly knowing that students have tried to memorize such a formula and failed, but I wouldn't be surprised if a lot of the wrong answers I've gotten from students on questions like this are based on such things.
Now, as a probabilist, I do have some use for calculus in my work. But I can't remember the last time I needed to know the volume of a solid of revolution.
Then again, my work is not particularly geometrical in nature.
So, I ask -- why do we spend so much time on this? Is this something that students actually need to know? I'm inclined to guess that it's just tradition. But at the same time I can't rule out that solids of revolution are actually so prevalent in engineering and physics (the traditional "customers" for the calculus course). Also, a lot of the "standard" calculus course seems to be a sequence of contrived problems that exist basically to make the student do various derivatives and integrals.