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  2. Square–cube law - Wikipedia

    en.wikipedia.org/wiki/Square–cube_law

    The square–cube law was first mentioned in Two New Sciences (1638). The square–cube law (or cube–square law) is a mathematical principle, applied in a variety of scientific fields, which describes the relationship between the volume and the surface area as a shape's size increases or decreases. It was first [dubious – discuss] described ...

  3. Surface area - Wikipedia

    en.wikipedia.org/wiki/Surface_area

    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 ...

  4. Lateral surface - Wikipedia

    en.wikipedia.org/wiki/Lateral_surface

    The lateral surface area is the area of the lateral surface. This is to be distinguished from the total surface area, which is the lateral surface area together with the areas of the base and top. For a cube the lateral surface area would be the area of the four sides. If the edge of the cube has length a, the area of one square face Aface = a ...

  5. Cube - Wikipedia

    en.wikipedia.org/wiki/Cube

    The surface area of a cube is six times the area of a square: [4] =. The volume of a cuboid is the product of length, width, and height. Because the edges of a cube are all equal in length, it is: [4] =. A unit cube is a special case where each cube's edge is 1 unit length. The surface area and the volume of a unit cube is 1.

  6. Surface-area-to-volume ratio - Wikipedia

    en.wikipedia.org/wiki/Surface-area-to-volume_ratio

    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.

  7. Area - Wikipedia

    en.wikipedia.org/wiki/Area

    Area is the measure of a region 's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object. Area can be understood as the amount of material with a given thickness that would be necessary to ...

  8. Parallelepiped - Wikipedia

    en.wikipedia.org/wiki/Parallelepiped

    In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms (the term rhomboid is also sometimes used with this meaning). By analogy, it relates to a parallelogram just as a cube relates to a square. [ a] Three equivalent definitions of parallelepiped are. a hexahedron with three pairs of parallel faces, a ...

  9. Octahedron - Wikipedia

    en.wikipedia.org/wiki/Octahedron

    The surface area of a regular octahedron can be ascertained by summing all of its eight equilateral triangles, whereas its volume is twice the volume of a square pyramid; if the edge length is , [4] =, =. The radius of a circumscribed sphere (one that touches the octahedron at all vertices), the radius of an inscribed sphere (one that tangent ...

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