For constants h,p> 0 let r = 2ph and consider the plane domain D in the first quadrant, bounded by x = 2py, x = 0 and y = h. (a) Show that the area of D is A = 2rh/3 and that the x-coordinate of its centroid is x = 3r/8. (b) Consider the solid paraboloid of revolution T of radius r and height h, obtained by revolving the plane domain D around the y-axis. Use the first theorem of Pappus to show that the volume of T is V = rh/2.