Surface area Surface area The surface area of a solid object is a measure of the total area that the surface of the object occupies. 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 flat polygonal faces), for which the surface area is the sum of the areas of its faces. Smooth surfaces, such as a sphere, are assigned surface area using their representation as parametric surfaces. This definition of surface area is based on methods
Menger sponge itself is the limit of this process after an infinite number of iterations. The "n"th stage of the Menger sponge, "M", is made up of 20 smaller cubes, each with a side length of (1/3). The total volume of "M" is thus (20/27). The total surface area of "M" is given by the expression 2(20/9) + 4(8/9). Therefore the construction's volume approaches zero while its surface area increases without bound. Yet any chosen surface in the construction will be thoroughly punctured as the construction continues, so that the limit is neither a solid nor a surface; it has a topological