Part B only.

(a) Sketch the following surfaces: (i) z = V1 -x2 - 12, (ii) kz = Vx2 + y2, where k is a positive constant. (b) Suppose the upper-half of the unit ball in R' is made of some heterogenous material with mass density & equal to M(x, y, z) = z at the point (x, y, Z). Let k be a positive constant, and consider the following portion of the upper-half of the unit ball: DK = { ( x, y, z) : 0 Vx2+ yz). According to the definition of density, the total mass in the region Dk is Mass(Dk) = W/, M(x, y. =). Using spherical coordinates, express Mass(Dk) as an iterated integral. You can evaluate the integral in (b), for example using WolframAlpha, to get TCK 2 Mass(Dk) = 4 (k2 + 1 ) (c) What is the relationship between the constant 7/4 and the upper hemisphere of the unit ball in this problem? Use this answer to find what value of k we need so our ice cream cone DK has exactly half of the mass of the upper hemisphere of the unit ball