The 2005 Extension 2 HSC contains a nice volume by cylindrical shells question.
What makes it even more interesting is the resulting answer. The volume is finite. All well and good, but this is a variation of the famous question often seen in a multi-variable calculus course, known as Gabriel's Trumpet or the Infinite Paint Can. Such a shape would have a finite volume, but an infinite surface area. It wouldn't be able to hold enought paint to paint the outside of the can!
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