Property of a Cissoid? 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?

I'm looking at the quote right now, and it must be wrong. The goblet is infinitely tall, with a radius of approximately 1, so it must have infinite area as well. The quote at the end by de Sluze refers to the weight being finite (proportional to the volume under the curve, above the x-axis), while the cup itself can hold an infinite volume. No matter how you play with this, the surface area must be infinite.
