Solid angle surface area of a spherical cap is always equal to the area of a circle whose radius equals the distance from the rim of the spherical cap to the point where the cap's axis of symmetry intersects the cap. In the diagram this radius is given as: Hence for a unit sphere the solid angle of the spherical cap is given as: When = , the spherical cap becomes a hemisphere having a solid angle 2. The solid angle of the complement of the cone (picture a melon with the cone cut out) is clearly: This is also the solid
Surface-area-to-volume ratio their biology, including their physiology and behavior. For example, many aquatic microorganisms have increased surface area to increase their drag in the water. This reduces their rate of sink and allows them to remain near the surface with less energy expenditure. An increased surface area to volume ratio also means increased exposure to the environment. The finely-branched appendages of filter feeders such as krill provide a large surface area to sift the water for food. Individual organs like the lung have numerous internal branchings that increase the surface area; in the case of the lung, the large surface supports gas