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

question 57

Multiple Choice

Find the area of the part of the hyperbolic paraboloid $z = y ^ { 2 } - x ^ { 2 }$ that lies between the cylinders $x ^ { 2 } + y ^ { 2 } = 1$ and $x ^ { 2 } + y ^ { 2 } = 16$ .

• A) \(\frac { 65 \sqrt { 65 } - 5 \sqrt { 5 } } { 3 } \pi\)
• B) \(\frac { \sqrt { 65 } - \sqrt { 5 } } { 6 } \pi\)
• C) \(\frac { 65 \sqrt { 65 } - 5 \sqrt { 5 } } { 6 } \pi\)
• D) \(\frac { \sqrt { 65 } - \sqrt { 5 } } { 3 } \pi\)
• E) \(\frac { 32 \sqrt { 65 } - 4 \sqrt { 5 } } { 3 } \pi\)

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Definitions:

Shape Style

Formatting options in graphic design and document editing software that allow customization of shapes’ visual appearance.

Shape Height

A property in graphical software that specifies the vertical dimension of a shape or object.

Shape Width

A property of graphical objects in computing that refers to the extent or measurement of an object's side-to-side dimension.

Cell Shading

A technique used in visual applications, such as spreadsheets and graphic design, to fill cells with solid colors or patterns to differentiate or highlight them.