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2. List of formulas in elementary geometry - Wikipedia

   en.wikipedia.org/wiki/List_of_formulas_in...

   List of formulas in elementary geometry. 2 languages. Français; ... This is a list of volume formulas of basic shapes: [4]: 405–406 ...

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

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

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

4. Volume - Wikipedia

   en.wikipedia.org/wiki/Volume

   In ancient times, volume was measured using similar-shaped natural containers. Later on, standardized containers were used. Some simple three-dimensional shapes can have their volume easily calculated using arithmetic formulas. Volumes of more complicated shapes can be calculated with integral calculus if a formula exists for the shape's boundary.

5. Simplex - Wikipedia

   en.wikipedia.org/wiki/Simplex

   The geometric simplex and simplicial complex should ... who wrote about these shapes in 1886 but ... Without the 1/n! it is the formula for the volume of an n ...

6. Octahedron - Wikipedia

   en.wikipedia.org/wiki/Octahedron

   The above shapes may also be realized as slices orthogonal to the long diagonal of a tesseract. If this diagonal is oriented vertically with a height of 1, then the first five slices above occur at heights r , ⁠ 3 / 8 ⁠ , ⁠ 1 / 2 ⁠ , ⁠ 5 / 8 ⁠ , and s , where r is any number in the range 0 < r ≤ ⁠ 1 / 4 ⁠ , and s is any number ...

7. Gabriel's horn - Wikipedia

   en.wikipedia.org/wiki/Gabriel's_horn

   Graph of = /. Gabriel's horn is formed by taking the graph of =, with the domain and rotating it in three dimensions about the x axis. The discovery was made using Cavalieri's principle before the invention of calculus, but today, calculus can be used to calculate the volume and surface area of the horn between x = 1 and x = a, where a > 1. [6]

8. Rhombicosidodecahedron - Wikipedia

   en.wikipedia.org/wiki/Rhombicosidodecahedron

   In geometry, the Rhombicosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces. It has 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, 60 vertices, and 120 edges.

9. 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.