Torricelli's Trumpet

When you plot the function y = 1/x, for 1 to infinity, the plot never touches the x axis. If you rotate this plot around the x axis, the horizontal asymptote, you get a solid which resembles a horn. This object is known as Torricelli's Trumpet or Gabriel's Horn. What makes this is a geometric solid particularly interesting is the fact that, mathematically it has a finite volume but infinite surface area. This means you could fill it with a finite amount of paint. However, it wouldn't be enough paint to cover the interior of the horn.