Suppose you make napkin rings by drilling holes with different diameters through two wooden balls (which also have different diameters). You discover that both napking rings have the same height h. Guess which ringhas more wood in it. Then use the shell method to compute the volume of a napking ring created by drilling a hole with radius r through the center of a sphere of radius R and express the answer in terms of h. Finally find the amount of wood in two different napkin rings: one with h=2in, r=.5in ,and R=1.5in. and the second napkin ring with h=2in, r=.75in, and R=2

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.3: Cylinders And Cones
Problem 39E
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Suppose you make napkin rings by drilling holes with different diameters through two wooden balls (which also have different diameters). You discover that both napking rings have the same height h. Guess which ringhas more wood in it. Then use the shell method to compute the volume of a napking ring created by drilling a hole with radius through the center of a sphere of radius and express the answer in terms of h. Finally find the amount of wood in two different napkin rings: one with h=2in, r=.5in ,and R=1.5in. and the second napkin ring with h=2in, r=.75in, and R=2.

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