Solve the Problem $\delta ( x , y , z ) = x y z$

Multiple Choice

Solve the problem.
-Find the center of mass of the rectangular solid of density $\delta ( x , y , z ) = x y z$ defined by $0 \leq x \leq 10,0 \leq y \leq 6,0 \leq z \leq 8$ .

A) $\bar { x } = \frac { 20 } { 3 } , \bar { y } = 4 , \bar { z } = \frac { 16 } { 3 }$
B) $\bar { x } = \frac { 5 } { 2 } , \bar { y } = \frac { 3 } { 2 } , \bar { z } = 2$
C) $\bar { x } = 5 , \bar { y } = 3 , \bar { z } = 4$
D) $\bar { x } = \frac { 10 } { 3 } , \bar { y } = 2 , \bar { z } = \frac { 8 } { 3 }$