Find the Surface Area of the Part of the Sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4$

Multiple Choice

Find the surface area of the part of the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4$ that lies above the plane z = 1.

A) $( 4 - 2 \sqrt { 2 } ) \pi$
B) 2
C) 2 $\pi$
D) 4 $\pi$
E) $( 8 - 4 \sqrt { 3 } ) \pi$
F) 6 $\pi$
G) 8 $\pi$
H) 16 $\pi$