Vuvuzelas and Surfaces of Revolution

Before the World Cup disappears forever (to me, four years = forever) , I must point out that the vuvuzela

reminds me a lot of the surface of revolution known as the Horn of Gabriel,

which is obtained by rotating the function around the x-axis.  The curious thing about this surface is that it has finite volume but infinite surface area.

Thus, if this object existed in the real world, you could fill it up with a finite amount of paint, but you couldn’t cover the surface with a finite amount of paint.  If that means anything.