Find the Area of the Part of the Hemisphere $z = \sqrt { 4 - x ^ { 2 } - y ^ { 2 } }$

Find the area of the part of the hemisphere $z = \sqrt { 4 - x ^ { 2 } - y ^ { 2 } }$ that lies above the area inside the circle $x ^ { 2 } + y ^ { 2 } = 1$ .

A) $( 4 - 2 \sqrt { 2 } ) \pi$

B) $( 6 - 3 \sqrt { 2 } ) \pi$

C) $( 8 - 4 \sqrt { 2 } ) \pi$

D) $( 6 - 3 \sqrt { 3 } ) \pi$

E) $( 8 - 4 \sqrt { 3 } ) \pi$

F) 6 $\pi$

G) 8 $\pi$

H) 16 $\pi$