Gabriel's horn:

the surface of revolution given by $1/x$

This has infinite surface area,
  (b/c $\int 1/x$)
but finite volume.
  (b/c $\int 1/x^2$)

Duh. Powers.

The paradox is stated as:
``You can fill it with paint but you can't paint it.'',
to which the explanation is rather:
``You can fill it with paint but you can't paint it -to uniform
  thickness-.''
(when you fill it with paint, the paint is very thin at the point)
