surface-to-volume ratio

Examples of surface-to-volume ratio in the following topics:

• Limiting Effects of Diffusion on Size and Development

  • An important concept in understanding the efficiency of diffusion as a transportation mechanism is the surface-to-volume ratio.
  • Recall that any three-dimensional object has a surface area and volume; the ratio of these two quantities is the surface-to-volume ratio.
  • The surface-to-volume ratio of a sphere is 3/r; as the cell gets bigger, its surface-to-volume ratio decreases, making diffusion less efficient .
  • The surface-to-volume ratio of a sphere decreases as the sphere gets bigger.
  • The surface area of a sphere is 4πr2 and it has a volume of (4/3)πr3 which makes the surface-to-volume ratio 3/r.

• Cell Size

  • Cell size is limited in accordance with the ratio of cell surface area to volume.
  • Therefore, as a cell increases in size, its surface area-to-volume ratio decreases.
  • The higher the surface area to volume ratio they have, the more effective this process can be.
  • Notice that as a cell increases in size, its surface area-to-volume ratio decreases.
  • The cell on the left has a volume of 1 mm3 and a surface area of 6 mm2, with a surface area-to-volume ratio of 6 to 1, whereas the cell on the right has a volume of 8 mm3 and a surface area of 24 mm2, with a surface area-to-volume ratio of 3 to 1.

• Characteristics of Prokaryotic Cells

  • The capsule enables the cell to attach to surfaces in its environment.
  • You may remember from your high school geometry course that the formula for the surface area of a sphere is 4πr2, while the formula for its volume is 4/3πr3.
  • Therefore, as a cell increases in size, its surface area-to-volume ratio decreases.
  • If the cell grows too large, the plasma membrane will not have sufficient surface area to support the rate of diffusion required for the increased volume.
  • Notice that as a cell increases in size, its surface area-to-volume ratio decreases.When there is insufficient surface area to support a cell's increasing volume, a cell will either divide or die.The cell on the left has a volume of 1 mm3 and a surface area of 6 mm2, with a surface area-to-volume ratio of 6 to 1, whereas the cell on the right has a volume of 8 mm3 and a surface area of 24 mm2, with a surface area-to-volume ratio of 3 to 1.

• Regulation of the Cell Cycle by External Events

  • Unlike the life of organisms, which is a straight progression from birth to death, the life of a cell takes place in a cyclical pattern.
  • When a daughter cell divides, it turns into two new cells, which would lead to the assumption that each cell is capable of being immortal as long as its descendants can continue to divide.
  • Both the initiation and inhibition of cell division are triggered by events external to the cell when it is about to begin the replication process.
  • Another factor that can initiate cell division is the size of the cell; as a cell grows, it becomes inefficient due to its decreasing surface-to-volume ratio.
  • The solution to this problem is to divide.

• Movement of Water and Minerals in the Xylem

  • Transpiration is the loss of water from the plant through evaporation at the leaf surface.
  • Transpiration is caused by the evaporation of water at the leaf, or atmosphere interface; it creates negative pressure (tension) equivalent to –2 MPa at the leaf surface.
  • The wet cell wall is exposed to the internal air space and the water on the surface of the cells evaporates into the air spaces.
  • This decreases the thin film on the surface of the mesophyll cells.
  • The leaves of a prickly pear are modified into spines, which lowers the surface-to-volume ratio and reduces water loss.

• Animal Bioenergetics

  • Smaller endothermic animals have a greater surface area for their mass than larger ones .
  • Torpor is a process that leads to a decrease in activity and metabolism, which allows animals to survive adverse conditions.
  • While endothermy is limited in smaller animals by surface-to-volume ratio, some organisms can be smaller and still be endotherms because they employ daily torpor during the part of the day that is coldest.
  • This allows them to conserve energy during the colder parts of the day when they consume more energy to maintain their body temperature.
  • The mouse has a much higher metabolic rate than the elephant since it has greater surface area relative to mass.

• The Respiratory System and Direct Diffusion

  • The primary function of the respiratory system is to deliver oxygen to the cells of the body's tissues and remove carbon dioxide.
  • As animal size increases, diffusion distances increase and the ratio of surface area to volume drops.
  • In other words, if the cell were very large or thick, diffusion would not be able to provide oxygen quickly enough to the inside of the cell.
  • Gas exchange by direct diffusion across surface membranes is efficient for organisms less than 1 mm in diameter.
  • The flat shape of these organisms increases the surface area for diffusion, ensuring that each cell within the body is close to the outer membrane surface and has access to oxygen.

• Lung Volumes and Capacities

  • The energy necessary to re-inflate the lung could be too great to overcome.
  • The residual volume is the only lung volume that cannot be measured directly because it is impossible to completely empty the lung of air.
  • The ratio of these values (FEV1/FVC ratio) is used to diagnose lung diseases including asthma, emphysema, and fibrosis.
  • If the FEV1/FVC ratio is high, the lungs are not compliant (meaning they are stiff and unable to bend properly); the patient probably has lung fibrosis.
  • It takes a long time to reach the maximal exhalation volume.

• The Work of Breathing

  • There are two ways to keep the alveolar ventilation constant: increase the respiratory rate while decreasing the tidal volume of air per breath (shallow breathing), or decrease the respiratory rate while increasing the tidal volume per breath.
  • By lowering the surface tension of the alveolar fluid, it reduces the tendency of alveoli to collapse.
  • Surfactant works like a detergent to reduce the surface tension, allowing for easier inflation of the airways.
  • They breathe at a very high lung volume to compensate for the lack of airway recruitment.
  • The ratio of FEV1 (the amount of air that can be forcibly exhaled in one second after taking a deep breath) to FVC (the total amount of air that can be forcibly exhaled) can be used to diagnose whether a person has restrictive or obstructive lung disease.

• Water’s Cohesive and Adhesive Properties

  • Cohesion allows for the development of surface tension, the capacity of a substance to withstand being ruptured when placed under tension or stress.
  • When a small scrap of paper is placed onto the droplet of water, the paper floats on top of the water droplet even though paper is denser (the mass per unit volume) than the water.
  • It's even possible to "float" a needle on top of a glass of water if it is placed gently without breaking the surface tension .
  • This pull results from the tendency of water molecules being evaporated on the surface of the plant to stay connected to water molecules below them, and so they are pulled along.
  • In another example, insects such as the water strider use the surface tension of water to stay afloat on the surface layer of water and even mate there.