Solve the Problem $z = \frac { 6 } { 7 } \sqrt { x ^ { 2 } + y ^ { 2 } }$

Multiple Choice

Solve the problem.
-Find the center of mass of the solid enclosed between the cone with equation $z = \frac { 6 } { 7 } \sqrt { x ^ { 2 } + y ^ { 2 } }$ and the plane with equation $z = 6$ if the density at any point is proportional to the distance from that point to the axis of the cone.

A) $( \bar { x } , \bar { y } , \bar { z } ) = \left( 0,0 , \frac { 9 } { 2 } \right)$
B) $( \overline { \mathrm { x } } , \overline { \mathrm { y } } , \overline { \mathrm { z } } ) = ( 0,0,4 )$
C) $( \bar { x } , \bar { y } , \bar { z } ) = \left( 0,0 , \frac { 15 } { 4 } \right)$
D) $( \overline { \mathrm { x } } , \overline { \mathrm { y } } , \overline { \mathrm { z } } ) = \left( 0,0 , \frac { 24 } { 5 } \right)$