Find the Mass of the Solid That Occupies the Region $x ^ { 2 } + y ^ { 2 } = 1$

Multiple Choice

Find the mass of the solid that occupies the region bounded by $x ^ { 2 } + y ^ { 2 } = 1$ , z = 2, and z = 0 and has density function $\rho ( x , y , z ) = z$ .

A) $\frac { \pi } { 4 }$

B) $\frac { \pi } { 3 }$

C) $\frac { \pi } { 2 }$

D) $\frac { 2 \pi } { 3 }$

E) $\frac { 3 \pi } { 4 }$

F) $\pi$

G) $\frac { 4 \pi } { 3 }$

H) 2 $\pi$