Consider the surface of revolution obtained by revolving the graph of f(x) = 1/x on the interval [1, [infinity]) about the x axis. (a) Show that the area of this surface is infinite. (b) Show that the volume of the solid of revolution bounded by this surface is finite. (c) The results of parts (a) and (b) suggest that one could fill the solid with a finite amount of paint, but it would take an infinite amount of paint to paint the surface. Explain this paradox. Next consider the surface of revolution obtained by revolving the curve y = 1/xʳ for x in [1, [infinity]) about the x axis. (d) For which values of r does this surface have finite area? (e) For which values of r does the solid surrounded by this surface have finite volume? Compute the volume for these values of r.