Find the Area of the Surface Given By $z = f ( x , y ) \text { over the region } R \text {. }$

Multiple Choice

Find the area of the surface given by $z = f ( x , y ) \text { over the region } R \text {. }$ $\begin{array} { l } f ( x , y ) = x y \\R = \left\{ ( x , y ) : x ^ { 2 } + y ^ { 2 } \leq 100 \right\}\end{array}$

A) $\frac { 2 } { 3 } ( 101 \sqrt { 101 } - 1 ) \pi$
B) $\frac { 2 } { 3 } ( 1 - 101 \sqrt { 101 } ) \pi$
C) $\frac { 2 } { 3 } ( 101 \sqrt { 101 } - 1 )$
D) $\frac { 3 } { 4 } ( 101 \sqrt { 101 } - 1 ) \pi$
E) $\frac { 2 } { 3 } ( 100 \sqrt { 101 } - 1 ) \pi$