Biological Sciences
Surface Area to Volume Ratio
Surface area to volume ratio is a measure of the amount of surface area per unit volume of an object. In biological sciences, this ratio is important because it affects the exchange of materials between a cell or organism and its environment. As the volume of an object increases, its surface area to volume ratio decreases, which can have implications for its ability to efficiently exchange materials.
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3 Key excerpts on "Surface Area to Volume Ratio"
eBook - PDFLife's Devices
The Physical World of Animals and Plants
- Steven Vogel(Author)
- 2020(Publication Date)
- Princeton University Press(Publisher)
LENGTHS, SURFACE AREAS, AND VOLUMES Without a doubt, nothing is more important in determining how size affects biological design than the relationship between surface area and volume. Contact between an organism and its surroundings is a function of its surface, while its internal processes and structure depend mainly on its volume. And the two do not maintain a simple proportionality— unless you change the shape of a body you cannot simultaneously double both its surface area and its volume. While perhaps not intuitively obvious, the situation can be easily illus-trated with a few quick and facile calculations. We use rules relating changes in length to changes in area and volume all the time, but we rarely recognize the underlying generalities. Consider cubes of different sizes (Figure 3.1). Surface area (S) and volume (V) are related to the length (/) of a side by the formulas: S = 6/ 2 and V = I 3 . (3.1) Now consider a set of spheres and the analogous formulas for surface area and volume in relation to radius (r): TABLE 3.1. THE RANGE OF SIZES WITHIN GENERAL CATEGORIES OF ORGANISMS Group Insects Fish Mammals Vascular plants Algae Length Range 10-4 to lO^m 10-2 to 10 + 1 m lO 1 to 10 + 2 m 10-2 to 10 + 2 m 10~ 5 to 10°m Factor 1000 1000 1000 10,000 100,000 39 CHAPTER 3 FIGURE 3.1. A pair of cubes. Each edge of the cube on the right is three times as long as an edge of the one on the left. The cube on the right has nine times the surface and no less than twenty-seven times the volume of the one on the left. 5 = 47T7-2 and V = 4>nr 3 /3. (3.2) And then imagine a set of circular cylinders (tuna fish cans, roughly) in which radius and height are equal (r = h). Their surface areas and volumes are S = 4irr 2 and V = TIT 3 . (3.3) In each case the formula for area specifies the length of something squared, and the formula for volume requires some length cubed.
eBook - PDFBiomedical Calculations
Principles and Practice
- Richard Burton(Author)
- 2008(Publication Date)
- Wiley(Publisher)
An important and general biological point arises from these relationships. With increasing size, the surface area of any object of constant proportions increases less steeply than the volume. Put another way, the surface/volume ratio falls with increasing size. For hypothetical cells and simple organisms of constant form and proportions, the ability to take up oxygen increases with surface area, while the oxygen consumption, one may postulate for the moment, increases with the volume (i.e. the amount of tissue). There is then a disadvantage to large size that may need to be offset by anatomical or physiological specializations aiding oxygen uptake. Similar considerations apply to the exchange of other materials. A large snowman may outlive a small one because the surface area for heat ex-change in the former is lower relative to the mass of snow. Relevant surfaces can include those of internal organs as well as those visible from outside. Such con-siderations suggest one should combine Eqs (11.9) and (11.10) to produce the following: surface area volume = k a k v . 1 L . (11.11) A DIGRESSION ON GRAPHS 105 In words, the ratio of surface area to volume is inversely proportional to L . We return to this simple conclusion later. 11.10 Replacing volumes with masses in these equations The discussion so far has involved volumes rather than masses, but it is mass that is more often measured. When density is constant, the two are exactly proportional to each other and mass is therefore often accepted as a replacement for volume, with, say, 1 g substituting for 1 cm 3 and 1 kg substituting for 1 L. With unit analysis in mind, we note, however, that the units differ. Let us therefore be more rigorous about this. To replace volumes with masses, recall that density equals mass per unit volume (i.e. mass/volume). Therefore, volume = mass density . (11.12) 11.12 Is this right? Check this formula by spelling out the units in terms of metres and kilograms.
eBook - PDF- Linda Almgren Kime, Judith Clark, Beverly K. Michael(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
Many large species have adapted by developing complex organs with convo- luted exteriors, thus greatly increasing the organsʼ surface areas. Human lungs, for instance, are heavily convoluted to increase the amount of surface area, thereby increasing the rate of exchange of gases. Stephen Jay Gould wrote that “the villi of our small intestine increase the surface area available for absorption of food.” (Villi are tiny finger‐like projections from the walls of the small intestine.) Body temperature also depends upon the ratio of surface area to volume. Animals gen- erate the heat needed for their volume by metabolic activity and lose heat through their skin surface. Small animals have more surface area in proportion to their volume than do large In Exploration 7.1 you can study further the effects of scaling up an object. Exploration Stephen Jay Gouldʼs essay “Size and Shape” in Ever Since Darwin: Reflections in Natural History offers an interesting perspective on the relationship between the size and shape of objects. Reading 2 For those who want to investigate how species have adapted and evolved over time, see D.W. Thompson, On Growth and Form (New York: Dover, 1992), and T. McMahon and J. Bonner, On Size and Life (New York: Scientific American Books, 1983). 7.1 The Tension Between Surface Area and Volume 381 Explore and Extend 7.1 Scaling Factors When a two‐ or three‐dimensional object is enlarged or shrunk, each linear dimension is multiplied by a constant called the scaling factor. For the two squares the scaling factor, F, is 3. That means that any linear measurement (for example, the length of the side or of the diagonal) is three times larger in the bigger square. Scaling up a Square by a Factor of 3 a. What is the relationship between the areas of the two squares? Show that for all squares F F area scaled (original area) where is the scaling factor 2 ⋅ = b.
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