In mathematics, a surface is any object that locally (if you zoom in close enough to it) looks like a piece of a flat plane. A sphere, a torus, a pseudosphere, and a Klein bottle are examples of different types of surface.
surface volume scaling law
By the surface volume scaling law, fine structures have relatively more surface to their volume. In the illustration here, each die weighs 2 g (0.07 oz) and has 9 cm2 (1.4 sq in) of surface. The sugar lump is made of 0.5 mm (0.02 in) grains and has about 200 cm2 (31 sq in) of total surface. The 2 g of "molecular sieve" on the watchglass is porous to the molecular level and has a remarkable 1,500 m2 (16,150 ft2) of total effective surface area.