Search results
Results from the WOW.Com Content Network
A sphere of radius r has surface area 4πr 2.. The surface area (symbol A) of a solid object is a measure of the total area that the surface of the object occupies. [1] The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with ...
Impervious surface percentage in various cities. The percentage imperviousness, commonly referred to as PIMP in calculations, is an important factor when considering drainage of water. It is calculated by measuring the percentage of a catchment area which is made up of impervious surfaces such as roads, roofs and other paved surfaces.
Graph of = /. Gabriel's horn is formed by taking the graph of =, with the domain and rotating it in three dimensions about the x axis. The discovery was made using Cavalieri's principle before the invention of calculus, but today, calculus can be used to calculate the volume and surface area of the horn between x = 1 and x = a, where a > 1. [6]
In differential geometry, the sign of the area of a region of a surface is associated with the orientation of the surface. [7] The area of a set A in differential geometry is obtained as an integration of a density : μ ( A ) = ∫ A d x ∧ d y , {\displaystyle \mu (A)=\int _{A}dx\wedge dy,} where d x and d y are differential 1-forms that make ...
In his work, Archimedes showed that the surface area of a cylinder is equal to: = + = (+). and that the volume of the same is: =. [3] On the sphere, he showed that the surface area is four times the area of its great circle. In modern terms, this means that the surface area is equal to:
The extension of the problem to higher dimensions (that is, for -dimensional surfaces in -dimensional space) turns out to be much more difficult to study.Moreover, while the solutions to the original problem are always regular, it turns out that the solutions to the extended problem may have singularities if .
However, plan commission member Jerry Pittsford said easements can be included, because the purpose of requiring open space is to limit a development’s impervious surface area to reduce flooding.
In mathematics, the Minkowski–Steiner formula is a formula relating the surface area and volume of compact subsets of Euclidean space.More precisely, it defines the surface area as the "derivative" of enclosed volume in an appropriate sense.