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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 ...
The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables r {\displaystyle r} is the radius, C = 2 π r {\displaystyle C=2\pi r} is the circumference (the length of any one of its great circles ),
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.
Both formulas can be determined by using Pythagorean theorem. The surface area of a cube is six times the area of a square: [4] =. The volume of a cuboid is the product of its length, width, and height. Because all the edges of a cube are equal in length, it is: [4] =.
The magnitude of an object's solid angle in steradians is equal to the area of the segment of a unit sphere, centered at the apex, that the object covers.Giving the area of a segment of a unit sphere in steradians is analogous to giving the length of an arc of a unit circle in radians.
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.
Scratches, represented by triangular-shaped grooves, make the surface area greater. 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).
A unit cube, more formally a cube of side 1, is a cube whose sides are 1 unit long. [ 1 ] [ 2 ] The volume of a 3-dimensional unit cube is 1 cubic unit, and its total surface area is 6 square units. [ 3 ]