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someone help me understand how do they come up with the surface area/volume ratio? (Biology-Cell)

someone help me understand how do they come up with the surface area/volume ratio? (Biology-Cell)

Human Anatomy & Physiology (11th Edition)
Human Anatomy & Physiology (11th Edition)
11th Edition
ISBN:9780134580999
Author:Elaine N. Marieb, Katja N. Hoehn
Publisher:Elaine N. Marieb, Katja N. Hoehn
Chapter1: The Human Body: An Orientation
Section: Chapter Questions
Problem 1RQ: The correct sequence of levels forming the structural hierarchy is A. (a) organ, organ system,...
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Screenshot for context. Can someone help me understand how do they come up with the surface area/volume ratio? (Biology-Cell)

**Evolutionary Adaptations Circumvent Cell Size Limits** There is an upper limit to cell size due to the change in the surface area-to-volume ratio of an object as its size increases (Figure 4.5). For example, doubling the diameter of a cell increases its volume by eight times but increases its surface area by only four times. The significance of this relationship is that the volume of a cell determines the amount of chemical activity that can take place within it, whereas the surface area determines the amount of substances that can be exchanged between the inside of the cell and the outside environment. Nutrients must enter cells constantly, and wastes must leave constantly. However, past a certain point, increasing the diameter of a cell gives a surface area that is insufficient to maintain an adequate nutrient–waste exchange for its entire volume. At that point cell growth must stop or the cell must divide to begin anew with a functional surface area-to-volume ratio. Some cells have adaptations that allow them to circumvent the surface area limitation just described. For instance, eggs of some species, such as birds and frogs, are much larger than **Figure 4.3** Units of measure and the ranges in which they are used in the study of molecules and cells. The vertical scale in each box is logarithmic. © Cengage Learning 2017
Transcribed Image Text:**Evolutionary Adaptations Circumvent Cell Size Limits** There is an upper limit to cell size due to the change in the surface area-to-volume ratio of an object as its size increases (Figure 4.5). For example, doubling the diameter of a cell increases its volume by eight times but increases its surface area by only four times. The significance of this relationship is that the volume of a cell determines the amount of chemical activity that can take place within it, whereas the surface area determines the amount of substances that can be exchanged between the inside of the cell and the outside environment. Nutrients must enter cells constantly, and wastes must leave constantly. However, past a certain point, increasing the diameter of a cell gives a surface area that is insufficient to maintain an adequate nutrient–waste exchange for its entire volume. At that point cell growth must stop or the cell must divide to begin anew with a functional surface area-to-volume ratio. Some cells have adaptations that allow them to circumvent the surface area limitation just described. For instance, eggs of some species, such as birds and frogs, are much larger than **Figure 4.3** Units of measure and the ranges in which they are used in the study of molecules and cells. The vertical scale in each box is logarithmic. © Cengage Learning 2017
**Relationship between Surface Area and Volume** The diagram illustrates the relationship between the surface area and volume of an object as it increases in size. As shown, the surface area of an object increases as a square of its linear dimension, whereas the volume increases as a cube of that dimension. - **Figure 4.5 Explanation:** - **Cubes with increasing sizes** (labeled as x, 2x, 3x, 4x) are visually represented. - **Total Surface Area** is calculated for each cube: - \(6x^2\), \(6(2x)^2 - 24x^2\), \(6(3x)^2 - 54x^2\), \(6(4x)^2 - 96x^2\). - **Total Volume** for each cube: - \(x^3\), \( (2x)^3 = 8x^3\), \( (3x)^3 = 27x^3\), \( (4x)^3 = 64x^3\). - **Surface Area/Volume Ratio:** - \(6:1\), \(3:1\), \(2:1\), \(1.5:1\). This table highlights how the surface area-to-volume ratio decreases as the size of an object increases. --- **Text Content:** Typical cells have a low surface area-to-volume ratio. This ratio is vital for understanding nutrient absorption and cell function. For example, large eggs store nutrients internally, minimizing the need for intake through the surface. After fertilization, rapid division helps form multicellular embryos. Some cells adapt by elongating or becoming thinner to increase surface area, like neurons and muscle cells. **Cell Structure and Function:** - **Organelles:** Small structures vital for cell function. - **Cytosol:** A water-based solution containing ions and organic molecules. - **Cytoskeleton:** Provides structural support and plays a crucial role in cell division and shape. Eukaryotic and prokaryotic cells share similar cytoskeletal proteins. Most cellular activities occur in the cytoplasm, including molecule synthesis for growth and reproduction. It also helps convert light and chemical energy into usable forms. Additionally, the cytoplasm facilitates signal conduction from the outside to the cell interior. **Diagram of a Phospholipid Molecule:** - Illustrates a phosphol
Transcribed Image Text:**Relationship between Surface Area and Volume** The diagram illustrates the relationship between the surface area and volume of an object as it increases in size. As shown, the surface area of an object increases as a square of its linear dimension, whereas the volume increases as a cube of that dimension. - **Figure 4.5 Explanation:** - **Cubes with increasing sizes** (labeled as x, 2x, 3x, 4x) are visually represented. - **Total Surface Area** is calculated for each cube: - \(6x^2\), \(6(2x)^2 - 24x^2\), \(6(3x)^2 - 54x^2\), \(6(4x)^2 - 96x^2\). - **Total Volume** for each cube: - \(x^3\), \( (2x)^3 = 8x^3\), \( (3x)^3 = 27x^3\), \( (4x)^3 = 64x^3\). - **Surface Area/Volume Ratio:** - \(6:1\), \(3:1\), \(2:1\), \(1.5:1\). This table highlights how the surface area-to-volume ratio decreases as the size of an object increases. --- **Text Content:** Typical cells have a low surface area-to-volume ratio. This ratio is vital for understanding nutrient absorption and cell function. For example, large eggs store nutrients internally, minimizing the need for intake through the surface. After fertilization, rapid division helps form multicellular embryos. Some cells adapt by elongating or becoming thinner to increase surface area, like neurons and muscle cells. **Cell Structure and Function:** - **Organelles:** Small structures vital for cell function. - **Cytosol:** A water-based solution containing ions and organic molecules. - **Cytoskeleton:** Provides structural support and plays a crucial role in cell division and shape. Eukaryotic and prokaryotic cells share similar cytoskeletal proteins. Most cellular activities occur in the cytoplasm, including molecule synthesis for growth and reproduction. It also helps convert light and chemical energy into usable forms. Additionally, the cytoplasm facilitates signal conduction from the outside to the cell interior. **Diagram of a Phospholipid Molecule:** - Illustrates a phosphol
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The surface area to volume ratio is very important. If it is too small, the cell will die. As a cell grows, its surface area to volume ratio decreases. At a certain point, this ratio becomes so small that the cell cannot live, so the cell must divide before this point is reached in order to return the surface area to volume ratio to an acceptable level again.

The surface area to volume ratio of an object will decrease as the size of the object increases. This means that a small object with a small volume will have a bigger surface area, as a proportion or fraction of the volume.

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