4. The object in Figure 2 is composed of the six bounding surfaces p =1, p = 2, z = 0, z = p, Q =0, and o = 57 /4. Figure 2: Two perspectives of a solid object, viewed from (left) above and (right) below and to the right. Using set notation to display the coordinate system, surface equation, and domains of the variables, the base has the definition $3 = {(p, , z) | z = 0, p E [1, 2], 0 E [0, 5x /4]}. (i) Using set notation and cylindrical coordinates, give definitions for the remaining five surfaces $1; $2. SA; $5: 56. The order of surfaces should match the order given above. (ii) The six surfaces enclose a volume. From the point of view of the enclosed volume, what are the outward pointing unit normals associated with the five surfaces $1, $2, Sa, So, Se? Label the respective unit vectors n1, n2, n3, n, ne and define them in terms of the cylindrical unit vectors. (iii) Using set notation redefine S4 in spherical coordinates, then give its outward pointing unit nor- mal n4 in terms of the spherical unit vectors. (iv) Using the coordinate transformation matrices given in the lecture notes, redefine n4 in terms of the cylindrical unit vectors