Solve the Problem $y$ -Axis the Area Bounded by the Curves $x ^ { 2 } - 25 y ^ { 2 } = 25 , x = 8$

question 177

Multiple Choice

Solve the problem.
-Find the volume generated by revolving about the $y$ -axis the area bounded by the curves: $x ^ { 2 } - 25 y ^ { 2 } = 25 , x = 8$

• A) \(\frac { 26 } { 5 } \pi \sqrt { 39 }\)
• B) \(\frac { 52 } { 5 } \pi \sqrt { 39 }\)
• C) \(\frac { 356 } { 15 } \pi \sqrt { 13 }\)
• D) \(\frac { 4 } { 5 } \pi \sqrt { 13 }\)

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Definitions:

Experimental Method

A research methodology involving the manipulation of variables to determine cause-and-effect relationships.

Cause-and-effect Conclusions

Deductive reasoning that connects an action or event (the cause) to outcomes or consequences (the effect), establishing a causal relationship.

Descriptive/Correlational Research

A research method that involves observing and describing the behavior of a subject without influencing it in any way, often used to identify patterns or relationships between variables.

Systematically Observes

Methodically and rigorously watching and recording phenomena or behaviors for analysis.