A layer of equal spheres is in the form of a square. The spheres are arranged so that each sphere is tangent to every one adjacent to it. In the spaces between sets of four adjacent spheres, other spheres rest, equal in size to the original. These spheres form in turn a second layer on top of the first. Successive layers of this sort form a pyramidal pile with a single sphere resting on top. If the bottom layer contains 16 spheres, what is the height of the pile in terms of the common radius r of the spheres.
A layer of equal spheres is in the form of a square. The spheres are arranged so that each sphere is tangent to every one adjacent to it. In the spaces between sets of four adjacent spheres, other spheres rest, equal in size to the original. These spheres form in turn a second layer on top of the first. Successive layers of this sort form a pyramidal pile with a single sphere resting on top. If the bottom layer contains 16 spheres, what is the height of the pile in terms of the common radius r of the spheres.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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A layer of equal spheres is in the form of a square. The spheres are arranged so that each sphere is tangent to every one adjacent to it. In the spaces between sets of four adjacent spheres, other spheres rest, equal in size to the original. These spheres form in turn a second layer on top of the first. Successive layers of this sort form a pyramidal pile with a single sphere resting on top. If the bottom
layer contains 16 spheres, what is the height of the pile in terms of the common radius r of the spheres.
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