Consider the surfaces Si = {(2,y, 2) | 2 +y = 4 -z, 0<2< 4} and Sz = {(z,y,2) | 2²+ y² s 4, z = 0} and the vector field v(z) = 6zi+ (4z +e")j+(5z+2*)k a) Calculate the volume of the region bounded by S, and S.. b) Calculate the flux of u through S, where the unit normal vector on S, is pointing upward. c) Use the results from parts b) and c) and the Gauss Theorem to calculate the flux of v through S1, where the unit normal vector on Si is pointing upward.

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