Solve the Problem $z = 4 - x ^ { 2 } - y ^ { 2 }$

Multiple Choice

Solve the problem.
-Find the center of mass of the hemisphere $z = 4 - x ^ { 2 } - y ^ { 2 }$ if the density is proportional to the distance from the center.

A) $\left( 0,0 , \frac { 6 } { 5 } \right)$
B) $\left( 0,0 , \frac { 16 } { 15 } \right)$
C) $\left( 0,0 , \frac { 4 } { 5 } \right)$
D) $\left( 0,0 , \frac { 14 } { 15 } \right)$