Math challenge!

Ok, you have two circles such as these: http://www.cut-the-knot.org/Outline/...gCircles.shtml

The bigger circle has the equation x^2+y^2=16. The smaller circle has a radius of 1. If we were to have the smaller circle go around the bigger one (as though the bigger one were a surface and the smaller one were a tire) and we kept track of a single point on the edge of the smaller tire and drew a dot on every point it touched on the plane, once the smaller tire had made a complete revolution around the bigger one, what would the total enclosed area be that the point on the smaller tire made?