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 exchange, bringing oxygen into the blood and releasing carbon dioxide from the blood. Similarly, the small intestine has a finely wrinkled internal surface, allowing the body to absorb nutrients efficiently. Cells can achieve a high surface area to volume ratio with an elaborately convoluted surface, like the microvilli lining the small intestine. Increased surface area can also lead to biological problems. More contact with the environment through the surface of a cell or an organ (relative to its volume) increases loss of water and dissolved substances. High surface area to volume ratios also present problems of temperature control in unfavorable