Find the Volume of the Indicated Region $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4$

question 236

Multiple Choice

Find the volume of the indicated region.
-the region bounded above by the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4$ and below by the cone $z = \sqrt { x ^ { 2 } + y ^ { 2 } }$

• A) \(2 \pi ( 2 - \sqrt { 2 } )\)
• B) \(2 \pi ( 2 - \sqrt { 3 } )\)
• C) \(\frac { 8 } { 3 } \pi ( 2 - \sqrt { 2 } )\)
• D) \(\frac { 8 } { 3 } \pi ( 2 - \sqrt { 3 } )\)

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Definitions:

Ectasis

An expansion or dilation of a hollow organ or vessel within the body.

Blasts

Immature cells, particularly seen in the blood or bone marrow, indicating early stages of cell development, often used in the context of leukemia.

Crine

Crine is a suffix used in biology and medicine to denote secreting, related to glands and substances they release, such as endocrine (hormone-secreting) or exocrine (substance-secreting through ducts).

Gen

Short for generation, referring to a distinct group within a defined time period sharing similar age and characteristics.