Suppose You Make Napkin Rings by Drilling Holes with Different $t$

question 34

Multiple Choice

Suppose you make napkin rings by drilling holes with different diameters through two wooden balls (which also have different diameters) . You discover that both napkin rings have the same height $t$ as shown in the figure. Use cylindrical shells to compute the volume of a napkin ring created by drilling a hole with radius $d$ through the center of a sphere of radius $D$ and express the answer in terms of $t$ .

• A) \(V = \frac { 1 } { 6 } \pi t ^ { 2 }\)
• B) \(V = \frac { 1 } { 3 } \pi t ^ { 2 }\)
• C) \(V = \frac { 1 } { 6 } \pi t ^ { 3 }\)
• D) \(V = \frac { 1 } { 3 } \pi t ^ { 3 }\)
• E) \(V = \frac { 1 } { 4 } \pi t ^ { 3 }\)

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Definitions:

Spinal Cord

A long, thin, tubular structure made up of nervous tissue, which extends from the brain and is encased within the vertebral column.

Acetylcholine

A neurotransmitter in both the central and peripheral nervous systems that plays a crucial role in muscle movement and cognitive functions.

Adrenaline

Also known as epinephrine, a hormone and neurotransmitter that increases heart rate, contracts blood vessels, dilates air passages, and participates in the fight-or-flight response of the sympathetic nervous system.

Nociception

The sensory nervous system's response to potentially harmful stimuli, signaling pain to the brain.