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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 area of one acre (red) superposed on an American football field (green) and Association football/soccer pitch (blue) 1 international acre is equal to the following metric units: 0.40468564224 hectare (A square with 100 m sides has an area of 1 hectare.) 4,046.8564224 square metres (or a square with approximately 63.61 m sides)
As the name suggests, an acre-foot is defined as the volume of one acre of surface area to a depth of one foot. Since an acre is defined as a chain by a furlong (i.e. 66 ft × 660 ft or 20.12 m × 201.17 m), an acre-foot is 43,560 cubic feet (1,233.5 m 3). There has been two definitions of the acre-foot (differing by about 0.0006%), using ...
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.
Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]
The curved surface area of the spherical segment bounded by two parallel disks is the difference of surface areas of their respective spherical caps. For a sphere of radius r {\displaystyle r} , and caps with heights h 1 {\displaystyle h_{1}} and h 2 {\displaystyle h_{2}} , the area is
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]
The material moves around in a playground as children play, [8] creating an uneven surface that is not wheelchair accessible. Wear areas under swings and at the base of slides are particularly prone to scuffing out. When this occurs, the thickness of the shredded rubber surface may not be enough to cushion falls from originally specified heights.