Solve the Problem $x ^ { 2 } + y ^ { 2 } - z ^ { 2 } = 0$

Multiple Choice

Solve the problem.
-The shape and density of a thin shell are indicated below. Find the coordinates of the center of mass.
Shell: cone $x ^ { 2 } + y ^ { 2 } - z ^ { 2 } = 0$ between $z = 1$ and $z = 4$
Density: constant

A) $\left( 0,0 , \frac { 127 } { 47 } \pi \right)$
B) $\left( 0,0 , \frac { 127 } { 47 } \right)$
C) $\left( 0,0 , \frac { 14 } { 5 } \pi \right)$
D) $\left( 0,0 , \frac { 14 } { 5 } \right)$