1. [-/1 Points] DETAILS 12.7.AE.05. MY NOTES EXAMPLE 5 Find the center of mass of a solid of constant density that is bounded by the parabolic cylinder x = 3y? and the planes x = z, z = 0, and x = 27. SOLUTION The solid E and its projection onto the xy-plane are shown in the figure. The lower and upper surfaces of E are the planes z = 0 and z = x, so we describe E as a type 1 region: E = { ( x, y, z) | | = y = , 3 y s x 5 27, 0szsx} Then, if the density is p(x, y, z) = p, the mass is m = J J J pov = [. J [ pdz dx dy 1x dy ITzip dy dy (729 - 9y )dy Because of the symmetry of E and p about the xz-plane, we can immediately say that Miz = 0 and therefore y = 0. The other moments are Myz p dv p dz dx dy dx dy 2p dy w / 2p