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

question 254

Multiple Choice

Find the volume of the indicated region.
-the region under the surface $z = x ^ { 2 } + y ^ { 4 }$ , and bounded by the planes $x = 0$ and $y = 16$ and the cylinder $y = x ^ { 2 }$

• A) \(\frac { 7,886,848 } { 165 }\)
• B) \(\frac { 125,851,648 } { 165 }\)
• C) \(\frac { 1,988,608 } { 165 }\)
• D) \(\frac { 31,479,808 } { 165 }\)

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Definitions:

Caldera

A large, bowl-shaped volcanic depression, formed by the collapse of land following a volcanic eruption or the emptying of a magma chamber.

Basin-shaped Depression

A rounded or oval valley or hollow in the Earth's surface, typically formed by erosion or the collapse of a volcanic crater.

Calderas

Large, basin-like depressions formed by the collapse of a volcano after a massive eruption, usually holding a lake.

Fissure Eruptions

Fissure eruptions are volcanic eruptions that occur through long, linear cracks in the Earth's surface, releasing lava and gases over a wide area.