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 the cured joint is machined flat. The same method is used to build up edge thickness, which can be profiled using tools and techniques similar to those used to work hardwoods. A major appeal of solid surface is its impermeability. Solid surface sinks can be joined to the countertop surface with no gaps, which eliminates areas for water to collect and bacteria to grow. Integral backsplashes can also be created that follow the contours of the wall “seamlessly” and without gaps. Should the material become scratched or broken, solid surface can, in most cases, be repaired quickly by a certified