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 smaller, regional manufacturers produce for local markets. Although solid surface faces competition from natural stone and engineered stone/quartz surfacing, the material is popular in Asia, particularly in residential new construction. An emerging market for solid surface is in commercial and industrial settings, where its non-porous characteristics, combined with durability, renewability and formability make it the material of choice for many designers and architects. Also appealing, is the wide range of colors and textures, as well as the ability to custom-color the material for large projects. Hospitals, in particular, employ large amounts of solid surface for sinks, showers, nursing stations and