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For a larger sphere, the band will be thinner but longer. In geometry, the napkin-ring problem involves finding the volume of a "band" of specified height around a sphere, i.e. the part that remains after a hole in the shape of a circular cylinder is drilled through the center of the sphere. It is a counterintuitive fact that this volume does ...
The volume of a n-ball is the Lebesgue measure of this ball, which generalizes to any dimension the usual volume of a ball in 3-dimensional space. The volume of a n -ball of radius R is where is the volume of the unit n -ball, the n -ball of radius 1. The real number can be expressed via a two-dimension recurrence relation.
Plot of the surface-area:volume ratio (SA:V) for a 3-dimensional ball, showing the ratio decline inversely as the radius of the ball increases. A solid sphere or ball is a three-dimensional object, being the solid figure bounded by a sphere. (In geometry, the term sphere properly refers only to the surface, so a sphere thus lacks volume in this ...
Stokes' law is the basis of the falling-sphere viscometer, in which the fluid is stationary in a vertical glass tube. A sphere of known size and density is allowed to descend through the liquid. If correctly selected, it reaches terminal velocity, which can be measured by the time it takes to pass two marks on the tube.
A Debye sphere is a volume whose radius is the Debye length. Debye length is an important parameter in plasma physics, electrolytes, and colloids (DLVO theory). The corresponding Debye screening wave vector for particles of density , charge at a temperature is given by in Gaussian units. Expressions in MKS units will be given below.
The exact definition varies: it is sometimes defined as the volume of a sphere with radius cH −1, or alternatively, a cube of side cH −1. Some cosmologists even use the term Hubble volume to refer to the volume of the observable universe, although this has a radius approximately three times larger.
Spherical trigonometry. The octant of a sphere is a spherical triangle with three right angles. Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, geodesics are great circles.
The intersection of a sphere with an elliptic or hyperbolic cylinder whose axis passes through the sphere center. The locus of points whose sum or difference of great-circle distances from a pair of foci is a constant. Many theorems relating to planar conic sections also extend to spherical conics.