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:

Human Capital

The capabilities, understanding, and expertise that an individual or group holds, considered in relation to their worth or expense to a company or nation.

Physical Capital

Assets used in the production process that are tangible in nature, such as machinery, buildings, and vehicles.

Proprietary Knowledge

Information that is not public and is owned by an individual or company, giving them a competitive advantage.

Public Goods

Goods that are neither excludable nor rival in consumption.