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 is priced to compete with natural stone or quartz surfacing. It is available in many colors and patterns. The material can be formed to shape, which makes it appealing to commercial and industrial designers. Specialist fabricators possess the skills and knowledge necessary to provide advice and customer service. Certain high-heat applications (anything above 400 F /200 C) are discouraged, due to the danger of cracking. Because scratches in solid surface appear white to the human eye, most dark colors are not recommended for high use areas. Solid surface Solid surface is a man-made material usually composed of a combination of