The Disk $( x - 4 ) ^ { 2 } + y ^ { 2 } \leq 1$

question 36

Multiple Choice

The disk $( x - 4 ) ^ { 2 } + y ^ { 2 } \leq 1$ is revolved about the $y$ -axis to generate a torus. Find its volume. (Hint: $\int _ { - 1 } ^ { 1 } \sqrt { 1 - y ^ { 2 } } d y = \frac { 1 } { 2 } \pi$ , since it is the area of a semicircle of radius 1 .)

• A) \(8 \pi ^ { 2 }\)
• B) \(2 \pi ^ { 2 }\)
• C) \(4 \pi ^ { 2 }\)
• D) \(4 \pi\)

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Definitions:

Adaptive Flexibility

The ability to adjust and modify one's behavior and thoughts in response to changing circumstances or environments.

Behavior Genetics

The academic discipline focused on analyzing how genetics and environmental factors impact behaviors.

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The process of managing one's behavior, emotions, and thoughts to achieve long-term goals.

Natural Selection

The process by which organisms better adapted to their environment tend to survive and produce more offspring, a fundamental concept in the theory of evolution by Charles Darwin.