Surface of revolution never negative, the area is given by If the curve is described by the function , , then the integral becomes for revolution around the -axis, and for revolution around the "y"-axis (using ). These come from the above formula. For example, the spherical surface with unit radius is generated by the curve , , when ranges over . Its area is therefore For the case of the spherical curve with radius , rotated about the -axis A minimal surface of revolution is the surface of revolution of the curve between two given points which minimizes surface area. A basic
Solid surface then injected into the cavity of the mould. Many finishes are available including, gel coated, matte, gloss, metallic and textured. A "surface fabricator" shapes and installs functional and decorative surfaces, usually in buildings. Surface fabrication, as a distinct professional enterprise, usually involves complex tasks of surface shaping. A leading case is countertop fabrication. For interior spaces, surfaces include solid coverings or decking for floors or walls, and countertops for kitchens, bathrooms, and workspaces. Natural surfaces are composed of naturally occurring materials like wood, stone, mineral, clay, gum and resin. Synthetic surfaces contain, in addition to any natural materials, man-made substances