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
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