A Surface Has the Shape of the Cone $z = \sqrt { x ^ { 2 } + y ^ { 2 } }$

Multiple Choice

A surface has the shape of the cone $z = \sqrt { x ^ { 2 } + y ^ { 2 } }$ between $z = 0$ and $z = 1$ with the density function $\rho ( x , y , z ) = 1 - z$ . Find the mass of the surface.

A) $\sqrt { 2 } \pi$
B) $\frac { \sqrt { 2 } \pi } { 3 }$
C) $6$

D) $1$
E) $2 \sqrt { 2 } \pi$
F) $2 \pi$
G) $\frac { 2 \sqrt { 2 } \pi } { 3 }$
H) $0$