I didn't think it was possible to have a finite area circumscribing an infinite volume but on page 89 of Nonplussed! by Havil (accessible for me at Google Books) it is claimed that such is the goblet-shaped solid generated by revolving the cissoid y$^2$ = x$^3$/(1-x) about the positive y-axis between this axis and the asymptote x = 1. What do you think?
Property of a Cissoid?
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calculus
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2What exactly are you asking? – 2011-01-25
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0I am asking if Havil is mistaken. – 2011-01-25
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0@ThudanBlunder: Then perhaps you should actually ask it? As, in the body of your question? – 2011-01-25
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1With a small bit of work (involving compact cut-offs and such) and some regularity assumptions on the boundary surface, you can actually show that the claim of a finite area surface bounding an infinite volume violates the [isoperimetric inequality](http://en.wikipedia.org/wiki/Isoperimetric_inequality#Isoperimetric_inequality_in_higher_dimensions). – 2011-01-25
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0@Arturo Magidin: Yes, you are right. I had a few things on my mind and suffered a lapse of concentration. 'What do you think?' is a silly question. – 2011-01-25
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0@Willie Wong: Coincidentally, I recently started a thread about the isoperimetrical quotient on another [url=http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_easy;action=display;num=1292959653]forum[/url], and so I ought to know the answer. But I thought I would see what the experts think, - sorry, I mean I would check with the experts. – 2011-01-25
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0That URL is http://tinyurl.com/6ej6k4b – 2011-01-25