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

question 123

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 $t$ .


Select the correct answer.

• 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:

Sensory Stimulus

Any object or event that is perceived by the senses, producing a response in the sensory organs and nervous system.

Zygote

The initial cell formed when two gamete cells are joined by means of sexual reproduction, marking the beginning of a new organism's development.

Fertilized Egg

A cell that results from the union of a sperm cell with an egg cell, marking the beginning of a new organism's development.

Teratogens

External agents such as chemicals, viruses, and radiation that can cause developmental abnormalities or birth defects in an embryo or fetus.