The Surface Area of the Surface Z = Xy in the First

Multiple Choice

The surface area of the surface z = xy in the first octant lying inside $x ^ { 2 } + y ^ { 2 } = 1$ is

A) $\frac { \pi ( 2 \sqrt { 2 } - 1 ) } { 3 }$
B) $\frac { \pi ( 2 \sqrt { 2 } - 1 ) } { 6 }$
C) $\frac { \pi ( 7 \sqrt { 21 } - 9 ) } { 6 }$
D) $\frac { \pi ( 7 \sqrt { 21 } - 1 ) } { 3 }$
E) $\frac { \pi ( 2 \sqrt { 2 } - 1 ) } { 2 }$