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The earliest explanation, given by Bergmann when originally formulating the rule, is that larger animals have a lower surface area to volume ratio than smaller animals, so they radiate less body heat per unit of mass, and therefore stay warmer in cold climates. Warmer climates impose the opposite problem: body heat generated by metabolism needs ...
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.
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. This principle applies to all solids. [3]
A composite cube with a side of 2 has a volume of 8 units 3 but a surface area of only 24 units 2. A rectangular prism two cubes wide, one cube long and four cubes tall has the same volume, but a surface area of 28 units 2. Stacking them in a single column gives 34 units 2.
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 ...
Specific surface area (SSA) is a property of solids defined as the total surface area (SA) of a material per unit mass, [1] (with units of m 2 /kg or m 2 /g). Alternatively, it may be defined as SA per solid or bulk volume [ 2 ] [ 3 ] (units of m 2 /m 3 or m −1 ).
The icosahedron has the largest number of faces and the largest dihedral angle, it hugs its inscribed sphere the most tightly, and its surface area to volume ratio is closest to that of a sphere of the same size (i.e. either the same surface area or the same volume).
The area density (also known as areal density, surface density, superficial density, areic density, mass thickness, column density, or density thickness) of a two-dimensional object is calculated as the mass per unit area. The SI derived unit is the "kilogram per square metre" (kg·m −2).