Solve the Problem $\delta ( x , y , z ) = \frac { 1 } { 36 - x ^ { 2 } - y ^ { 2 } }$

Multiple Choice

Solve the problem.
-Find the center of mass of the region of density $\delta ( x , y , z ) = \frac { 1 } { 36 - x ^ { 2 } - y ^ { 2 } }$ bounded by the paraboloid $z = 36 - x ^ { 2 } - y ^ { 2 }$ and the $x y$ -plane.

A) $\bar { x } = 0 , \bar { y } = 0 , \bar { z } = 2$
B) $\bar { x } = 0 , \bar { y } = 0 , \bar { z } = 6$
C) $\bar { x } = 0 , \bar { y } = 0 , \bar { z } = 3$
D) $\bar { x } = 0 , \bar { y } = 0 , \bar { z } = \frac { 1 } { 2 }$