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  2. 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 ...

  3. 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

  4. Sphericity - Wikipedia

    en.wikipedia.org/wiki/Sphericity

    Defined by Wadell in 1935, [1] the sphericity, , of an object is the ratio of the surface area of a sphere with the same volume to the object's surface area: = where is volume of the object and is the surface area.

  5. Square–cube law - Wikipedia

    en.wikipedia.org/wiki/Square–cube_law

    Its volume would be multiplied by the cube of 2 and become 8 m 3. The original cube (1 m sides) has a surface area to volume ratio of 6:1. The larger (2 m sides) cube has a surface area to volume ratio of (24/8) 3:1. As the dimensions increase, the volume will continue to grow faster than the surface area. Thus the square–cube law.

  6. Pappus's centroid theorem - Wikipedia

    en.wikipedia.org/wiki/Pappus's_centroid_theorem

    The theorem applied to an open cylinder, cone and a sphere to obtain their surface areas. The centroids are at a distance a (in red) from the axis of rotation.. In mathematics, Pappus's centroid theorem (also known as the Guldinus theorem, Pappus–Guldinus theorem or Pappus's theorem) is either of two related theorems dealing with the surface areas and volumes of surfaces and solids of ...

  7. File:Comparison of surface area vs volume of shapes.svg

    en.wikipedia.org/wiki/File:Comparison_of_surface...

    Graphs of surface area, A against volume, V of all 5 Platonic solids and a sphere by CMG Lee, showing that the surface area decreases for rounder shapes, and the surface-area-to-volume ratio decreases with increasing volume. The dashed lines show that when the volume increases 8 (2³) times, the surface area increases 4 (2²) times.

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