Find the Area of the Surface for the Portion of the Paraboloid

question 34

Multiple Choice

Find the area of the surface for the portion of the paraboloid $z = 64 - x ^ { 2 } - y ^ { 2 }$ in the first Octant.

• A) \(\frac { \pi } { 24 } ( 257 \sqrt { 257 } - 1 )\)
• B) \(\frac { \pi } { 40 } ( 513 \sqrt { 513 } - 3 )\)
• C)\(\frac { \pi } { 48 } ( 65 \sqrt { 65 } - 3 )\) d.
• D)\(\frac { \pi } { 48 } ( 515 \sqrt { 515 } - 3 )\)
• E)\(\frac { \pi } { 40 } ( 65 \sqrt { 65 } - 1 )\)

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Definitions:

Self-Disclosure

The sharing of information about oneself.

Xiao

In Confucian philosophy, the virtue of filial piety or respect towards one’s parents and ancestors.

Social Interdependence

A theory suggesting that the outcomes for individuals in any situation are determined by the actions and decisions of others, emphasizing the importance of cooperative goals over competitive ones.

Individualistic Cultures

Societies that emphasize personal achievements, independence, and a self-oriented focus, as opposed to collective goals and interdependence.