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 $x ^ { 2 } + y ^ { 2 } = 36$ .

A) $( 1297 \sqrt { 1297 } + 5 \sqrt { 5 } ) \pi$
B) $( 1297 \sqrt { 1297 } - 6 \sqrt { 5 } ) \pi$
C) $\frac { 1 } { 9 } ( 1297 \sqrt { 1297 } - 6 \sqrt { 5 } ) \pi$
D) $\frac { 1 } { 9 } ( 1297 \sqrt { 1297 } - 5 \sqrt { 5 } )$
E) $\frac { 1 } { 9 } ( 1297 \sqrt { 1297 } - 5 \sqrt { 5 } ) \pi$