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For most practical purposes, the volume inside a sphere inscribed in a cube can be approximated as 52.4% of the volume of the cube, since V = π / 6 d 3, where d is the diameter of the sphere and also the length of a side of the cube and π / 6 ≈ 0.5236.
A sphere has 2/3 the volume and surface area of its circumscribing cylinder. A sphere and cylinder were placed on the tomb of Archimedes at his request. Archimedes ( c. 287 BCE – c. 212 BCE ), a colorful figure about whom many historical anecdotes are recorded, is remembered along with Euclid as one of the greatest of ancient mathematicians.
The summary chart includes the five largest worldwide automotive manufacturing groups as of 2017 by number of vehicles produced. Those same groups held the top 5 positions 2007 to 2019; Hyundai Motor Group had a lower rank until it took the fifth spot in 2007 from the at that time split German-American auto manufacturer DaimlerChrysler, while Ford became surpassed by Honda in 2020, and even ...
In this two-volume treatise addressed to Dositheus, Archimedes obtains the result of which he was most proud, namely the relationship between a sphere and a circumscribed cylinder of the same height and diameter. The volume is 4 / 3 π r 3 for the sphere, and 2 π r 3 for the cylinder.
The Kelvin problem on minimum-surface-area partitions of space into equal-volume cells, and the optimality of the Weaire–Phelan structure as a solution to the Kelvin problem [73] Lebesgue's universal covering problem on the minimum-area convex shape in the plane that can cover any shape of diameter one [74]
Portable Document Format (PDF), standardized as ISO 32000, is a file format developed by Adobe in 1992 to present documents, including text formatting and images, ...
In a suspension of solid particles (e.g. micron-size spheres suspended in oil), an effective viscosity can be defined in terms of stress and strain components which are averaged over a volume large compared with the distance between the suspended particles, but small with respect to macroscopic dimensions. [59]
Sound passes through the system by compressing and expanding the springs, transmitting the acoustic energy to neighboring spheres. This helps transmit the energy in-turn to the neighboring sphere's springs (bonds), and so on. The speed of sound through the model depends on the stiffness/rigidity of the springs, and the mass of the spheres. As ...