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He established analogous results for the sphere showing that the volume of a sphere is equal to that of a cone whose height equals the radius of the sphere and whose base equals its surface area; the surface area of the sphere he found to be four times the area of its greatest circle.
The radius of each sphere is equal to the time the acoustic wave travels from the source to the detector multiplied with the speed of sound.
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The width of the green border and the diameter of the armillary sphere are equal to 1/8 and 3/7 of the side's dimension, respectively.
Steradian, unit of solid-angle measure in the International System of Units (SI), defined as the solid angle of a sphere subtended by a portion of the surface whose area is equal to the square of the sphere's radius.
Thus, for the 3-mm sphere RCavg is equal to RCmax.
Accordingly, Srolovitz et al. proposed the following formulation to obtain a sphere whose volume is equal to the original Voronoi volume [33]: V i = 4 π 3 a i 3 a i = ∑ j r i j − 1 2 ∑ j r i j − 2 (2).
Depending on the amino acid type, the length of this vector is made equal to the radius of a sphere whose volume is equal to the average volume occupied by this type of amino acid.
For hollow spheres, the geometrical radius is equal to the radius of gyration, r g = d geo.
The radius of the outside particle decreases to R. The average gyration radius is r and the average density is ρ R. Since mass is conserved in the above process, the mass of the sphere in the perfect crystal is equal to the mass of the outside particle.
In other words, at F o), the effective polarizability, χ eff), of the sphere (the polarizability of sphere minus the polarizability of the medium) is equal to zero.
This is defined as the ratio of particle volume over total volume of the circumscribing sphere and, for agglomerated debris particles, it is equal to 0.236.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com