Question:

If the volume of a cube is 8, what is the total surface area of the cube?

Answer:

The volume, or amount of space inside a box is h * W * L.The surface area of a box is found by calculating: 2* h * W + 2* L * h + 2* w * L. Volume 8 surface area 24.

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Geometry
Euclidean geometry

Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated by earlier mathematicians, Euclid was the first to show how these propositions could fit into a comprehensive deductive and logical system. The Elements begins with plane geometry, still taught in secondary school as the first axiomatic system and the first examples of formal proof. It goes on to the solid geometry of three dimensions. Much of the Elements states results of what are now called algebra and number theory, explained in geometrical language.

For more than two thousand years, the adjective "Euclidean" was unnecessary because no other sort of geometry had been conceived. Euclid's axioms seemed so intuitively obvious (with the possible exception of the parallel postulate) that any theorem proved from them was deemed true in an absolute, often metaphysical, sense. Today, however, many other self-consistent non-Euclidean geometries are known, the first ones having been discovered in the early 19th century. An implication of Einstein's theory of general relativity is that physical space itself is not Euclidean, and Euclidean space is a good approximation for it only where the gravitational field is weak.

Cubes Volume Area
Surface area

The surface area of a solid object is the total area of the object's faces and curved surfaces. 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 flat polygonal faces), for which the surface area is the sum of the areas of its faces. Smooth surfaces, such as a sphere, are assigned surface area using their representation as parametric surfaces. This definition of surface area is based on methods of infinitesimal calculus and involves partial derivatives and double integration.

A general definition of surface area was sought by Henri Lebesgue and Hermann Minkowski at the turn of the twentieth century. Their work led to the development of geometric measure theory, which studies various notions of surface area for irregular objects of any dimension. An important example is the Minkowski content of a surface.


Planck's law

Planck's law describes the electromagnetic radiation that pervades any medium, whatever its constitution, that is in thermodynamic equilibrium at a definite temperature. If the medium is of homogeneous and isotropic constitution, then the radiation is homogeneous, isotropic, unpolarized, and incoherent. The law is named after Max Planck, who originally proposed it in 1900. It is a pioneer result of modern physics and quantum theory.

For frequency ν, or for wavelength λ, Planckian radiation can be described thus:


Four-dimensional space

In mathematics, four-dimensional space ("4D") is an abstract concept derived by generalizing the rules of three-dimensional space. It has been studied by mathematicians and philosophers for over two centuries, both for its own interest and for the insights it offered into mathematics and related fields.

Algebraically it is generated by applying the rules of vectors and coordinate geometry to a space with four dimensions. In particular a vector with four elements (a 4-tuple) can be used to represent a position in four-dimensional space. The space is a Euclidean space, so has a metric and norm, and so all directions are treated as the same: the additional dimension is indistinguishable from the other three.

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