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2. 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

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. Area - Wikipedia

   en.wikipedia.org/wiki/Area

   The formula for the surface area of a sphere is more difficult to derive: because a sphere has nonzero Gaussian curvature, it cannot be flattened out. The formula for the surface area of a sphere was first obtained by Archimedes in his work On the Sphere and Cylinder. The formula is: [6] A = 4πr 2 (sphere), where r is the radius of the sphere.

5. Surface (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Surface_(mathematics)

   The graph of a continuous function of two variables, defined over a connected open subset of R 2 is a topological surface. If the function is differentiable, the graph is a differentiable surface. A plane is both an algebraic surface and a differentiable surface. It is also a ruled surface and a surface of revolution.

6. Square–cube law - Wikipedia

   en.wikipedia.org/wiki/Square–cube_law

   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 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.

7. On the Sphere and Cylinder - Wikipedia

   en.wikipedia.org/wiki/On_the_Sphere_and_Cylinder

   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: