Solve the Problem $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 49$

Multiple Choice

Solve the problem.
-Find the centroid of the region bounded above by the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 49$ and below by the plane $z = 2$ if the density is constant.

A) $\bar { x } = 0 , \bar { y } = 0 , \bar { z } = \frac { 363 } { 64 }$
B) $\bar { x } = 0 , \bar { y } = 0 , \bar { z } = \frac { 243 } { 80 }$
C) $\bar { x } = 0 , \bar { y } = 0 , \bar { z } = \frac { 243 } { 64 }$
D) $\bar { x } = 0 , \bar { y } = 0 , \bar { z } = 12$