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) $\frac { 1 } { 9 } ( 1297 \sqrt { 1297 } - 5 \sqrt { 5 } ) \pi$

Question

Quizplus · Accepted Answer

The area of the surface can be found using the surface integral formula for a function $z = f(x, y)$. The integral is evaluated over the region between the two cylinders, and the correct choice is based on the calculation of this integral.

Find the Area of the Part of Hyperbolic Paraboloid z=y2−x2z = y ^ { 2 } - x ^ { 2 }z=y2−x2

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