6. A torus of revolution (doughnut) is obtained by rotating a circle C in the xz plane about the z-axis. Suppose that C has a radius r and center (R,0,0). (a) Find a parametrization r(u, v) of the torus. Specify the set D in which (u, v) must lie. Hint: You can choose let u represent the angle that the line from the point r(u, v) on the torus to the center of the rotated circle form with the xy-plane, and let v denote the angle formed by the line from the point r(u, v) on the torus to the origin with the positive x-axis. See figures below. 0 R- (b) Show that the surface area of the torus is 4x2 Rr.