Use Polar Coordinates to Find the Volume of the Solid $z = x ^ { 2 } + y ^ { 2 }$

question 116

Multiple Choice

Use polar coordinates to find the volume of the solid under the paraboloid $z = x ^ { 2 } + y ^ { 2 }$ and above the disk $x ^ { 2 } + y ^ { 2 } \leq 9$ .

• A) \(81 \pi\)
• B) \(162 \pi\)
• C) \(324 \pi\)
• D) \(27 \pi\)
• E) \(40.5 \pi\)

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Definitions:

Crista Galli

A vertical protrusion of the ethmoid bone in the brain that serves as an attachment point for the falx cerebri, a membrane that divides the two cerebral hemispheres.

Styloid Process

A pointed piece of bone that extends from the temporal bone of the skull, serving as an attachment point for muscles and ligaments of the tongue and neck.

Frontal

Referring to the forehead or the front part of something, particularly in anatomy, it pertains to the front part of the brain or the frontal bone of the skull.

Maxilla

A pair of bones forming the upper jaw and part of the orbits surrounding the eyes, essential for facial structure.