Solid angle orientation formula_9, and distance from the viewer as: where the surface area of a sphere is . The solid angle of a cone with its apex at the apex of the solid angle, and with apex angle 2, is the area of a spherical cap on a unit sphere For small such that , this reduces to the area of a circle . The above is found by computing the following double integral using the unit surface element in spherical coordinates: This formula can also be derived without the use of calculus. Over 2200 years ago Archimedes proved that the
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