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For example, a cube with a side length of 1 meter has a surface area of 6 m 2 and a volume of 1 m 3. If the sides of the cube were multiplied by 2, its surface area would be multiplied by the square of 2 and become 24 m 2. Its volume would be multiplied by the cube of 2 and become 8 m 3.
The surface-area-to-volume ratio has physical dimension inverse length (L −1) and is therefore expressed in units of inverse metre (m-1) or its prefixed unit multiples and submultiples. As an example, a cube with sides of length 1 cm will have a surface area of 6 cm 2 and a volume of 1 cm 3. The surface to volume ratio for this cube is thus
The cube is also the number multiplied by its square: n 3 = n × n 2 = n × n × n. The cube function is the function x ↦ x 3 (often denoted y = x 3) that maps a number to its cube. It is an odd function, as (−n) 3 = −(n 3). The volume of a geometric cube is the cube of its side length, giving rise to the
Cubic hectometre. the volume of a cube of side length one hectometre (100 m) equal to a gigalitre. in civil engineering abbreviated MCM for million cubic metres. 1 hm 3 = 1 000 000 m3 = 1 GL. Cubic kilometre. the volume of a cube of side length one kilometre ( 1000 m) equal to a teralitre.
Cube root. In mathematics, a cube root of a number x is a number y such that y3 = x. All nonzero real numbers have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots. For example, the real cube root of 8, denoted , is 2, because 23 = 8, while the other ...
The ratio of a regular dodecahedron's volume to the volume of a cube embedded inside such a regular dodecahedron is 1 : 2 / 2 + ϕ, or 1 + ϕ / 2 : 1, or (5 + √ 5) : 4. For example, an embedded cube with a volume of 64 (and edge length of 4), will nest within a regular dodecahedron of volume 64 + 32ϕ (and edge length of 4ϕ − 4).
The term unit cube or unit hypercube is also used for hypercubes, or "cubes" in n-dimensional spaces, for values of n other than 3 and edge length 1. Sometimes the term "unit cube" refers in specific to the set [0, 1] n of all n-tuples of numbers in the interval [0, 1].
In geometry, a cube [a] is a three-dimensional solid object bounded by six square faces, facets, or sides, with three meeting at each vertex. Viewed from a corner, it is a hexagon and its net is usually depicted as a cross. [1] The cube is the only regular hexahedron and is one of the five Platonic solids.