Find the Area of the Part of Hyperbolic Paraboloid $z = y ^ { 2 } - x ^ { 2 }$

Multiple Choice

Find the area of the part of hyperbolic paraboloid $z = y ^ { 2 } - x ^ { 2 }$ that lies between the cylinders $x ^ { 2 } + y ^ { 2 } = 1$ and $x ^ { 2 } + y ^ { 2 } = 9$ .

A) $( 82 \sqrt { 82 } - 3 \sqrt { 5 } ) \pi$
B) $( 82 \sqrt { 82 } + 5 \sqrt { 5 } ) \pi$
C) $\frac { 2 } { 9 }$ $( 82 \sqrt { 82 } - 5 \sqrt { 5 } )$
D) $\frac { 2 } { 9 }$ $( 82 \sqrt { 82 } - 3 \sqrt { 5 } ) \pi$
E) $\frac { 2 } { 9 }$ $( 82 \sqrt { 82 } - 5 \sqrt { 5 } ) \pi$