Solve the Problem $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 36$

Multiple Choice

Solve the problem.
-Find the center of mass of the region of constant density bounded from above by the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 36$ and from below by the cone $z = \sqrt { x ^ { 2 } + y ^ { 2 } }$ .

A) $\bar { x } = 0 , \bar { y } = 0 , \bar { z } = \frac { 9 } { 4 } ( 2 + \sqrt { 2 } )$
B) $\bar { x } = 0 , \bar { y } = 0 , \bar { z } = \frac { 21 } { 8 } ( 2 + \sqrt { 2 } )$
C) $\bar { x } = 0 , \bar { y } = 0 , \bar { z } = \frac { 15 } { 8 } ( 2 + \sqrt { 2 } )$
D) $\bar { x } = 0 , \bar { y } = 0 , \bar { z } = \frac { 9 } { 8 } ( 2 + \sqrt { 2 } )$