Title: Surface-area-to-volume ratio
Content:   The ratio between the surface area and volume of cells and organisms has an enormous impact on 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 exchange, bringing oxygen into 
Title: Surface area
Content:  The surface area of an organism is important in several considerations, such as regulation of body temperature and digestion. Animals use their teeth to grind food down into smaller particles, increasing the surface area available for digestion. The epithelial tissue lining the digestive tract contains microvilli, greatly increasing the area available for absorption. Elephants have large ears, allowing them to regulate their own body temperature. In other instances, animals will need to minimize surface area; for example, people will fold their arms over their chest when cold to minimize heat loss. The surface area to volume ratio (SA:V) of a cell imposes upper limits on size, as the volume increases much faster than does 
Title: Surface-area-to-volume ratio
Content:  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 environments. The surface to volume ratios of organisms of different sizes also leads to some biological rules such as Allen's rule, Bergmann's rule  and gigantothermy.
Title: Gas exchange
Content:  is very large, and adequate for its gas-exchange needs without further modification. However, as an organism increases in size, its surface area and volume do not scale in the same way. Consider an imaginary organism that is a cube of side-length, L. Its volume increases with the cube (L3) of its length, but its external surface area increases only with the square (L2) of its length. This means the external surface rapidly becomes inadequate for the rapidly increasing gas-exchange needs of a larger volume of cytoplasm. Additionally, the thickness of the surface that gases must cross (dx in Fick's Law) can also be larger in larger organisms: in the case of a single-celled organism, a typical cell membrane is only 10 nm thick; but in larger organisms such as roundworms (Nematoda) the equivalent exchange surface - the cuticle - is substantially thicker at 0.5 μm.
Title: Surface-area-to-volume ratio
Content:  The surface-area-to-volume ratio, also called the surface-to-volume ratio and variously denoted sa/vol or SA:V, is the amount of surface area per unit volume of an object or collection of objects. SA:V is an important concept in science and engineering. It is used to explain the relation between structure and function in processes occurring through the surface AND the volume. Good examples for such processes are processes governed by the heat equation, i.e., diffusion and heat transfer by conduction. SA:V is used to explain the diffusion of small molecules, like Oxygen and Carbon dioxide between air, blood and cells, Water loss by animals, bacterial morphogenesis, organism's Thermoregulation, design of artificial bone tissue, artificial lungs and many more biological and biotechnological structures. For more examples see Glazier. The relation between SA:V and diffusion 
Title: Gill
Content:  Many microscopic aquatic animals, and some larger but inactive ones, can absorb sufficient oxygen through the entire surface of their bodies, and so can respire adequately without gills. However, more complex or more active aquatic organisms usually require a gill or gills. Many invertebrates, and even amphibians, use both the body surface and gills for gaseous exchange. Gills usually consist of thin filaments of tissue, lamellae (plates), branches, or slender, tufted processes that have a highly folded surface to increase surface area. The delicate nature of the gills is possible because the surrounding water provides support. The blood or other body fluid must be in intimate contact with the respiratory surface for ease of diffusion. A high surface area is crucial to the gas exchange of aquatic organisms, as 
Title: Gas exchange
Content:  gas exchange membrane is typically the cell membrane. Some small multicellular organisms, such as flatworms, are also able to perform sufficient gas exchange across the skin or cuticle that surrounds their bodies. However, in most larger organisms, which have a small surface-area to volume ratios, specialised structures with convoluted surfaces such as gills, pulmonary alveoli and spongy mesophyll provide the large area needed for effective gas exchange. These convoluted surfaces may sometimes be internalised into the body of the organism. This is the case with the alveoli, which form the inner surface of the mammalian lung, the spongy mesophyll, which is found inside the leaves of some kinds of plant, 
Title: Gas exchange
Content:   In multicellular organisms therefore, specialised respiratory organs such as gills or lungs are often used to provide the additional surface area for the required rate of gas exchange with the external environment. However the distances between the gas exchanger and the deeper tissues are often too great for diffusion to meet gaseous requirements of these tissues. The gas exchangers are therefore frequently coupled to gas-distributing circulatory systems, which transport the gases evenly to all the body tissues regardless of their distance from the gas exchanger. Some multicellular organisms such as flatworms (Platyhelminthes) are relatively large but very thin, allowing their outer body surface to act as a gas exchange surface without the need for a specialised 
Title: Surface-area-to-volume ratio
Content: On Being the Right Size, J.B.S. Haldane 
Title: Surface-area-to-volume ratio
Content:  heat conduction rate is explained from flux and surface perspective, focusing on the surface of a body as the place where diffusion, or heat conduction, takes place, i.e., the larger the SA:V there is more surface area per unit volume through which material can diffuse, therefore, the diffusion or heat conduction, will be faster. Similar explanation appears in the literature: "Small size implies a large ratio of surface area to volume, thereby helping to maximize the uptake of nutrients across the plasma membrane", and elsewhere. For a given volume, the object with the smallest surface area (and therefore with the smallest SA:V) is a ball, a consequence of the isoperimetric inequality in 3 dimensions. By contrast, objects with acute-angled spikes will have very large surface area for a given volume.

Question: surface area in many kinds of organs is important because the amount of surface determines?
Answer: effective gas exchange.