Solve the Problem $( \bar { x } , \bar { y } , \bar { z } ) = \left( 0,0 , \frac { 16 } { 5 } \frac { 1 } { \pi } \right)$

Multiple Choice

Solve the problem.
-Find the center of mass of the upper half of a solid ball of radius 3 centered at the origin if the density at any point is proportional to the distance from that point to the z-axis.

A) $( \bar { x } , \bar { y } , \bar { z } ) = \left( 0,0 , \frac { 16 } { 5 } \frac { 1 } { \pi } \right)$
B) $( \bar { x } , \bar { y } , \bar { z } ) = \left( 0,0 , \frac { 3 } { 8 } ( 1 + \sqrt { 2 } ) \right)$
C) $( \bar { x } , \bar { y } , \bar { z } ) = \left( 0,0 , \frac { 6 } { 5 } \right)$
D) $( \bar { x } , \bar { y } , \bar { z } ) = \left( 0,0 , \frac { 3 } { 8 } \pi \right)$