The Surface Area of the Surface $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 36$

Multiple Choice

The surface area of the surface $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 36$ lying within $x ^ { 2 } + y ^ { 2 } = 9$ is

A) $\pi ( 144 - 72 \sqrt { 3 } )$
B) $\pi ( 144 - 72 \sqrt { 5 } )$
C) $\pi ( 144 - 71 \sqrt { 3 } )$
D) $\pi ( 144 - 71 \sqrt { 5 } )$
E) $\pi ( 144 - 70 \sqrt { 3 } )$