Solve the Problem $z = \frac { 7 } { 8 } \sqrt { x ^ { 2 } + y ^ { 2 } }$

Multiple Choice

Solve the problem.
-Find the center of mass of the solid enclosed between the cone with equation $z = \frac { 7 } { 8 } \sqrt { x ^ { 2 } + y ^ { 2 } }$ and the plane with equation $z = 7$ if the density at any point is proportional to the distance from that point to the plane $z = 7$ .

A) $( \bar { x } , \bar { y } , \bar { z } ) = \left( 0,0 , \frac { 21 } { 5 } \right)$
B) $( \overline { \mathrm { x } } , \overline { \mathrm { y } } , \overline { \mathrm { z } } ) = \left( 0,0 , \frac { 14 } { 3 } \right)$
C) $( \bar { x } , \bar { y } , \bar { z } ) = \left( 0,0 , \frac { 49 } { 12 } \right)$
D) $( \bar { x } , \bar { y } , \bar { z } ) = \left( 0,0 , \frac { 35 } { 8 } \right)$