Use Polar Coordinates to Find the Volume of the Solid $x ^ { 2 } + y ^ { 2 } = 16$

question 6

Multiple Choice

Use polar coordinates to find the volume of the solid inside the cylinder $x ^ { 2 } + y ^ { 2 } = 16$ and the ellipsoid $2 x ^ { 2 } + 2 y ^ { 2 } + z ^ { 2 } = 64$ .

• A) \(943.21\)
• B) \(843.21\)
• C) \(1,043.21\)
• D) \(793.21\)
• E) \(693.21\)

---

Definitions:

Deterministic

The philosophical concept that suggests all events, including moral choices, are completely determined by previously existing causes.

Neurotic Anxiety

A type of anxiety stemming from unconscious conflicts that threaten to surface, often manifesting as irrational fears or behaviors.

Id

In psychoanalytic theory, the part of the mind that is the source of instinctive impulses that seek satisfaction in accordance with the pleasure principle.

Superego

The aspect of personality that acts as a moral center, guiding behavior with internalized ideals, values, and standards for right and wrong.