$\text { Write a double integral that represents the surface area of } f ( x , y ) = 12 - x ^ { 2 } - y ^ { 2 }$

Multiple Choice

$\text { Write a double integral that represents the surface area of } f ( x , y ) = 12 - x ^ { 2 } - y ^ { 2 }$ over the region $R : R = \{ ( x , y ) : 0 \leq x \leq 4,0 \leq y \leq 4 \}$ . Use a computer algebra system to evaluate the double integral. Round your answer to four decimal places.

A) $4.5062$
B) $140.1398$
C) $37.8613$
D) $99.5824$
E) $13.6778$