Screenshot for context. Can someone help me understand how do they come up with the surface area/volume ratio? (Biology-Cell) Evolutionary Adaptations CircumventCell Size LimitsThere is an upper limit to cell size due to the change in thesurface area-to-volume ratio of an object as its size increases(Figure 4.5). For example, doubling the diameter of a cellincreases its volume by eight times but increases its surfacearea by only four times. The significance of this relationship isthat the volume of a cell determines the amount of chemicalactivity that can take place within it, whereas the surface areadetermines the amount of substances that can be exchangedbetween the inside of the cell and the outside environment.Nutrients must enter cells constantly, and wastes must leaveconstantly. However, past a certain point, increasing thediameter of a cell gives a surface area that is insufficient tomaintain an adequate nutrient-waste exchange for its entirevolume. At that point cell growth must stop or the cell mustdivide to begin anew with a functional surface area-to-volumeratio.Some cells have adaptations that allow them to circumventthe surface area limitation just described. For instance, eggs ofsome species, such as birds and frogs, are much larger thanFIGURE 4.3 Units of measure and the ranges in which they areused in the study of molecules and cells. The vertical scale in each boxis logarithmic.ⒸCengage Leaming 2017 Total surfaceareaTotalvolumeSurface area/volume ratio6x²x³6:16(2x)²-24x²(2x)³-8x³3:16(3x)² - 54x²(3x)³ = 27x³2:16(4x)²-96x²contains the organelles, the cytosol, and the cyto-skeleton. The organelles ("little organs") are small,organized structures important for cell function.The cytosol is an aqueous (water) solution con-taining ions and various organic molecules. Thecytoskeleton is a protein-based framework of fila-mentous structures that, among other things, helpsmaintain proper cell shape and plays key roles incell division and chromosome segregation from cellgeneration to cell generation. The cytoskeleton wasonce thought to be specific to eukaryotes, butresearch has shown that all major eukaryotic cyto-skeletal proteins have functional equivalents inprokaryotes.Many of the cell's vital activities occur in thecytoplasm, including the synthesis and assembly ofmost of the molecules required for growth andreproduction (except those made in the centralregion) and the conversion of chemical and light.energy into forms that can be used by cells. Thecytoplasm also conducts stimulatory signals from the outsideinto the cell interior and carries out chemical reactions thatrespond to these signals.(4x)³ = 64x³1.5:1FIGURE 4.5 Relationship between surface area and volume. The surface area ofan object increases as a square of the linear dimension, whereas the volume increases asa cube of that dimension.ⒸCengage Leaming 2017typical cells, meaning that they have a low surface area-to-volume ratio. In this case the eggs contain a large store of nutri-ents so no nutrients need to be brought into the cells. Inaddition, once fertilized, the eggs divide rapidly to produce amulticelled embryo with each cell of typical cell size (see Chap-ter 50). Another adaptation to circumvent the surface area lim-itation is for cells to be long and thin, or skinny and flat, bothof which increase surface area. Examples are nerve cells (neu-rons; see Chapter 39) and muscle cells (see Chapter 43). Yetanother adaptation is seen in human intestinal cells, whichhave closely packed, fingerlike extensions that increase theirsurface area (see Chapter 47).-Hydrophilichead-HydrophobictailPhospholipidmoleculeATT

Question

Screenshot for context. Can someone help me understand how do they come up with the surface area/volume ratio? (Biology-Cell) Evolutionary Adaptations CircumventCell Size LimitsThere is an upper limit to cell size due to the change in thesurface area-to-volume ratio of an object as its size increases(Figure 4.5). For example, doubling the diameter of a cellincreases its volume by eight times but increases its surfacearea by only four times. The significance of this relationship isthat the volume of a cell determines the amount of chemicalactivity that can take place within it, whereas the surface areadetermines the amount of substances that can be exchangedbetween the inside of the cell and the outside environment.Nutrients must enter cells constantly, and wastes must leaveconstantly. However, past a certain point, increasing thediameter of a cell gives a surface area that is insufficient tomaintain an adequate nutrient-waste exchange for its entirevolume. At that point cell growth must stop or the cell mustdivide to begin anew with a functional surface area-to-volumeratio.Some cells have adaptations that allow them to circumventthe surface area limitation just described. For instance, eggs ofsome species, such as birds and frogs, are much larger thanFIGURE 4.3 Units of measure and the ranges in which they areused in the study of molecules and cells. The vertical scale in each boxis logarithmic.ⒸCengage Leaming 2017 Total surfaceareaTotalvolumeSurface area/volume ratio6x²x³6:16(2x)²-24x²(2x)³-8x³3:16(3x)² - 54x²(3x)³ = 27x³2:16(4x)²-96x²contains the organelles, the cytosol, and the cyto-skeleton. The organelles (&#34;little organs&#34;) are small,organized structures important for cell function.The cytosol is an aqueous (water) solution con-taining ions and various organic molecules. Thecytoskeleton is a protein-based framework of fila-mentous structures that, among other things, helpsmaintain proper cell shape and plays key roles incell division and chromosome segregation from cellgeneration to cell generation. The cytoskeleton wasonce thought to be specific to eukaryotes, butresearch has shown that all major eukaryotic cyto-skeletal proteins have functional equivalents inprokaryotes.Many of the cell's vital activities occur in thecytoplasm, including the synthesis and assembly ofmost of the molecules required for growth andreproduction (except those made in the centralregion) and the conversion of chemical and light.energy into forms that can be used by cells. Thecytoplasm also conducts stimulatory signals from the outsideinto the cell interior and carries out chemical reactions thatrespond to these signals.(4x)³ = 64x³1.5:1FIGURE 4.5 Relationship between surface area and volume. The surface area ofan object increases as a square of the linear dimension, whereas the volume increases asa cube of that dimension.ⒸCengage Leaming 2017typical cells, meaning that they have a low surface area-to-volume ratio. In this case the eggs contain a large store of nutri-ents so no nutrients need to be brought into the cells. Inaddition, once fertilized, the eggs divide rapidly to produce amulticelled embryo with each cell of typical cell size (see Chap-ter 50). Another adaptation to circumvent the surface area lim-itation is for cells to be long and thin, or skinny and flat, bothof which increase surface area. Examples are nerve cells (neu-rons; see Chapter 39) and muscle cells (see Chapter 43). Yetanother adaptation is seen in human intestinal cells, whichhave closely packed, fingerlike extensions that increase theirsurface area (see Chapter 47).-Hydrophilichead-HydrophobictailPhospholipidmoleculeATT

Accepted Answer

The surface area to volume ratio is very important. If it is too small, the cell will die. As a cell…