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

question 60

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

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Definitions:

Friction

The resistance that one surface or object encounters when moving over another, often generating heat.

Immobilize

To restrict the movement of a part of the body or an object, often to prevent further injury or to allow healing.

Action

The process of doing something, typically to achieve an aim or to deal with a problem.

RICE

Abbreviation for rest, ice, compression, elevation, referring to the treatment for sprains and strains.