To receive full credit you must show your work - answers are not enough. 1. Calculating the following using spherical coordinates. (a) Calculate the total charge inside a sphere of radius 3 (centered at the origin) if the charge density is v(r, y, =) = in uC/em. vaz+ y'+ 2 (b) Calculate the mass of the spherical wedge of the unit sphere which lies between zy-plane and the oz-plane with a density of 6(x, y, 2) = y, in kg/m. (c) Calculate the volume of the part of the ball a + y' + 2' S 4 above the plane = = 1. 2. The following integral is written in cylindrical coordinates; write the integral in spherical coordinates. ( You do not have to evaluate.) 3. Calculate the following integrals using whatever coordinate system is most appropriate. (a) Calculate dA where R is the region between a ty? = 1 and a ty' = 9 and between r = 0 and y = r. (b) Calculate / (1 + 4ry) dA, where D is the region bounded by y = 2 and y = 3.. (c) Calculate / vaz + 22 dV, where Q is the region bounded by the paraboloid y = 4 - 28 - 2 and the x2-plane. 4. Find the center of mass of the lamina occupying the top-half of the disk a2 + y'