The Surface Area of the Surface $x ^ { 2 } + y ^ { 2 } = 3 z$

Multiple Choice

The surface area of the surface $x ^ { 2 } + y ^ { 2 } = 3 z$ lying within $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4 z$ is

A) $\frac { \pi ( 7 \sqrt { 21 } - 5 ) } { 6 }$
B) $\frac { \pi ( 7 \sqrt { 21 } - 7 ) } { 6 }$
C) $\frac { \pi ( 7 \sqrt { 21 } - 9 ) } { 6 }$
D) $\frac { \pi ( 7 \sqrt { 21 } - 11 ) } { 6 }$
E) $\frac { \pi ( 7 \sqrt { 21 } - 13 ) } { 6 }$