hello welcome back and in this next mini video we are going to be answering the questions why are cells so small so in order to illustrate the answer to this question I have drawn three cells and in this bad illustration these are three cubes of different dimensions so here is a one millimeter Cube so it's one millimeter by one millimeter by one millimeter length width depth Etc okay here's a two millimeter Cube and here is a much bigger Cube of 10 millimeter Dimensions note that this is not to scale Okay so the short answer to this question why are cells so small is because answer the problem of the surface area to volume ratio okay and so the short answer to this question is that as the larger cells get the smaller the surface area to volume ratio and conversely the smaller the cells are the larger the surface area to volume ratio okay so we're going to talk about what that means momentarily but let's take a look at this first mathematically all right so how do you determine the surface area of a cube well it's given by a pretty simple mathematical equation which I'm sure you've learned about in Geometry or in high school algebra maybe you haven't seen this in a long time so let's refresh your memories okay so the surface area of a cube is length times width okay for just one face of the cube but how many faces does a cube have six right so 6 times length times width and for the one millimeter Cube that's a pretty simple equation 6 times 1 times 1. and that gives us a cube with Dimensions or with measurements of dimensions of six millimeters squared okay because we're looking at the two dimensional surface area of all of these sides of the cube okay so what is it for the two milliliter Cube 6 times 2 times 2 or in other words six times two squared that gives us what okay so 6 times 4 equals 24. Square millimeters that's how many millimeters there are for the surface area for this entire Cube all right now for the much much larger Cube It's 6 times 10 squared that gives us a total surface area of what 100 times 6 00 millimeters squared okay so we're not done with figuring out the surface area let's also figure out the volume so the volume of a cube is given by the equation length times width times height okay so for the one millimeter Cube that's pretty easy one times one times one equals well one right for the two milliliter Cube two times two times two in other words 2 to the third power is eight millimeters cubed okay oops let's fix this one millimeter cubed okay now for the large Cube ten times ten times ten ten cubed equals one thousand millimeters cubed okay so millimeter squared gives us surface area two dimensions for three dimensional for three dimensional space millimeters cubed okay now the problem is going to refer back to the surface area to volume ratio of these cells of different sizes so what is the surface area to volume ratio of the one millimeter Cube six over one for the two millimeter Cube 24 over 8 and that reduces to three to one right for the 10 millimeter Cube 600 over a thousand let's see if we reduce that down that's six over ten or three over five okay so now this which one has the largest surface area of volume ratio it's the smallest right at six to one and as the cubes get larger three to one three over five and even larger cubes we get smaller and smaller and smaller and smaller fractions of the surface area to volume ratio all right so that's all well and good as far as mathematically but let's flip this around real quick whoops I guess we can't flip this around you guys can just look at me like that so what does this mean for cells all right so imagine you're going to a party and you have to get ice all right so you know that a leader block of ice okay is comes in a leader bag but you can also get a liter of chipped ice or shaved ice all right now it's they're both equal a liter of that frozen water that ice right but which one is going to melt faster so in other words which ice the leader block of ice or the leader chopped ice is going to melt faster so to think about this physically so let's see if we can think about heat diffusing or permeating those ice all right that ice either the block ice or the chipped ice which ice is going to melt faster well of course it's going to be the chipped ice right and that's because of the problem of the surface area to volume ratio those much much smaller chips of ice they're going to allow the heat to permeate them and diffuse into them much much faster than that big block of ice okay well that's the ice example but let's think about this in terms of cells okay if a cell is trying to get nutrients from its environments into which cells are you going to more easily diffuse those nutrients smaller cells right so that's why cells are so small it's this problem of the surface area to the volume ratio the larger the cell is the more difficult it is to diffuse nutrients and gases and whatnot into that cell where it needs to be right until next time