Surface area in the study of fractals. Extensions of the notion of area which partially fulfill its function and may be defined even for very badly irregular surfaces are studied in geometric measure theory. A specific example of such an extension is the Minkowski content of the surface. The below given formulas can be used to show that the surface area of a sphere and cylinder of the same radius and height are in the ratio 2 : 3, as follows. Let the radius be "r" and the height be "h" (which is 2"r" for the sphere). formula_7 The discovery of this
Surface area a certain class of surfaces that satisfies several natural requirements. The most fundamental property of the surface area is its additivity: "the area of the whole is the sum of the areas of the parts". More rigorously, if a surface "S" is a union of finitely many pieces "S", …, "S" which do not overlap except at their boundaries, then Surface areas of flat polygonal shapes must agree with their geometrically defined area. Since surface area is a geometric notion, areas of congruent surfaces must be the same and the area must depend only on the shape of the surface,