Sketch the Solid Bounded by the Graphs of the Equations $z = x ^ { 2 } + y ^ { 2 }$

question 33

Essay

Sketch the solid bounded by the graphs of the equations $z = x ^ { 2 } + y ^ { 2 }$ and $z = 50 - x ^ { 2 } - y ^ { 2 }$ , and then use a triple integral to find the volume of the solid.

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Definitions:

Intuitions

Intuitions are immediate understandings, knowledge, or beliefs that come without the need for conscious reasoning.

Explicit Conscious

Direct, clear awareness of mental activities, such as thinking, feeling, and decision-making.

Effortless

Achieved with remarkable ease and without apparent difficulty or exertion.

Representativeness Heuristic

A mental shortcut that involves making judgments about the probability of an event under uncertainty, based on how much it resembles the typical case.