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

question 100

Multiple Choice

Find the volume of the indicated region.
-the region that lies under the paraboloid $z = x ^ { 2 } + y ^ { 2 }$ and above the triangle enclosed by the lines $x = 8 , y = 0$ , and $y = 2 x$

• A) \(\frac { 1792 } { 3 }\)
• B) 8192
• C) \(\frac { 14,336 } { 3 }\)
• D) \(\frac { 224 } { 3 }\)

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Definitions:

Accompanying Figure

An illustration, chart, graph, or image that is provided alongside a text to complement, explain, or exemplify the information being discussed.

Nitrogenous Waste

Waste products containing nitrogen, such as ammonia, urea, or uric acid, produced by the metabolism of proteins and nucleic acids.

Freshwater Fishes

A diverse group of fish species that spend most or all of their lives in freshwater habitats such as lakes, rivers, and ponds, contrasting with saltwater or marine fishes.

Ammonia

A colorless gas with a characteristic pungent smell, NH3, used in industrial and cleaning products and produced by living organisms during metabolism.