Solve the Problem $x ^ { 2 } + y ^ { 2 } = 2 z$

Multiple Choice

Solve the problem.
-The shape and density of a thin shell are indicated below. Find the coordinates of the center of mass.
Shell: "nose" of the paraboloid $x ^ { 2 } + y ^ { 2 } = 2 z$ cut by the plane $z = 3$
Density: $\delta = \sqrt { x ^ { 2 } + y ^ { 2 } + 1 }$

A) $\left( 0,0 , \frac { 15 } { 8 } \right)$
B) $\left( 0,0 , \frac { 96 } { 11 } \right)$
C) $\left( 0,0 , \frac { 9 } { 11 } \right)$
D) $( 0,0,8 )$