An Upper Hemisphere Is Given By $z = \sqrt { 16 - x ^ { 2 } - y ^ { 2 } }$

Multiple Choice

An upper hemisphere is given by $z = \sqrt { 16 - x ^ { 2 } - y ^ { 2 } }$ with the density function $\rho ( x , y , z ) = z$ . Find the mass of the sphere.

A) $32 \pi$
B) $8 \pi$
C) $64 \pi$
D) $1$
E) $16 \pi$
F) $4 \pi$
G) $\frac { 32 \pi } { 3 }$
H) $\frac { 64 \pi } { 3 }$