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 such as metal alloys or polymers. Solid surfaces are synthetic surfaces manufactured from polymeric materials. Tools of surface fabrication include routers, drills, templates, clamps, ovens, suction cup grips, and table saws. Larger surface fabricators may also use CNC routers. For all but the simplest jobs, surface fabrication usually takes place in the workshop, after which the finished product is assembled and installed at the work site. Installation of multi-part surfaces, such as "L" and "U" shaped countertops, often involves complex work with specialized tools, to create a seamless result. Solid surfaces is used in the following environment : Solid surface