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
Surface and bulk erosion of two separate categories. In surface erosion, the erosion rate is directly proportional to the surface area of the material. For very thin materials, the surface area remains relatively constant when the material degrades, which allows surface erosion to be characterized as zero order release since the rate of degradation is constant. In bulk erosion, the erosion rate depends on the volume of the material. Due to degradation, the volume of the material decreases during bulk erosion causing the erosion rate to decrease over time. Therefore, bulk erosion rates are difficult to control since it is not zero order. To