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

question 137

Short Answer

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 $t$ .

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Definitions:

Prohibited

Forbidden by law, rules, or other forms of authority.

Infringes

The act of violating, breaching, or encroaching upon laws, regulations, contracts, or the rights of others.

Production Possibilities Curve

A graphical representation showing the maximum combination of goods or services that can be produced with a given set of resources and technology.

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The manner of achieving a goal or completing a task with the minimum waste of time and effort.