Wednesday, 2 April 2014

2005 Extension 2 HSC Volumes Question

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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