This lesson is called Diffusion and surface area to volume ratio and is from the unit Transport and exchange surfaces in humans.

Hi there, my name's Mrs. McCready, and I'm here to guide you through today's lesson.

So thank you very much for joining me.

I hope you're looking forward to it.

In our lesson today, we're going to calculate the surface area volume and surface area to volume ratio of different sized cubes, and we're going to observe how long it takes for a liquid to diffuse into them.

So we're going to come across a good number of keywords in our lesson today, and they're shown there on the screen for you now.

You may wish to pause the video to make a note of them, but I will introduce them to you as we come across them.

So in our lesson today, we are going to firstly calculate surface area, volume, and their ratio.

And then we're going to have a look at the rate of diffusion in cubes.

So, are you ready? I am.

Let's get started.

Now, surface area is the total area of the surface of the organism and it can be calculated used in the equation width times height times the number of faces, in this case, of a cube.

So if we have an organism which we assume to be a perfect cube, such as this bacterium, if it has a width of two micrometres, its surface area is width times height times number of faces.

So two times two times six.

So its surface area is 24 micrometres squared.

The volume of an object is the total matter inside the surface.

And we can calculate the volume of a cube by timesing width by height by depth.

So if we take our cube-shaped bacterium with a width of two micrometres, its volume, width times height times depth, is two by two by two.

So two times two times two is eight.

And so the total volume of our cube-shaped bacterium is eight micrometres cubed.

Now, we can compare the surface area and volume as a ratio.

So we have seen that for a bacterium with a width of two micrometres, its surface area is 24 micrometres squared and its volume is eight micrometres cubed.

So its surface area to volume ratio is 24 to eight, which we can simplify down to three to one.

So its surface area to volume ratio, in simplest terms, is three to one.

So let's calculate these together then.

Let's calculate firstly the surface area to volume ratio of a bacterium cube with a width of three micrometres.

So the surface area is width times height times the number of faces, which is three by three by six.

Three by three by six is 54 micrometre squared.

So the surface area of this bacterium cube is 54 micrometre squared.

Now let's calculate the volume.

So the volume is width times height times depth.

So that's three by three by three.

And that equals 27.

So the volume is 27 micrometres cubed.

So now let's compare that as a ratio.

A surface area to volume ratio of 54 to 27, which we can simplify down to two to one.

So that's my workings.

Now I would like you to have a go and calculate the surface area to volume ratio for a bacterium cube with a height of six micrometres.

Remember to show all of your workings.

I'll give you five seconds, but you will need longer, so you may need to pause the video.

Okay, let's see how you got on then.

So to calculate surface area, we're doing width times height times the number of faces.

So for a bacterium cube with a height of six micrometres, we're timesing six by six by six.

And that equals 216 micrometres squared.

Now to calculate the volume, we're timesing width by height by depth.

So that's also six times six times six, and therefore the volume is also 216, but this time the units are micrometres cubed.

So let's compare the surface area to volume ratio.

Surface area to volume ratio is 216 to 216, and we can simplify that down to one to one.

So just check over your workings.

Did you get all of those correct? Well done if you did.

So let's compare these bacterial cubes.

So we're going from a bacterium with a width of three micrometres to a width of six micrometres.

In other words, we're doubling the width.

Now, if we double the width, what happens to the surface area? Well, going from 54 to 216 is a multiplication of four, so the surface area has increased by four.

What about the width then? Well, to go from 27 to 216 is actually an eightfold increase.

We're timesing that by eight.

And what about the ratio then? Well, the ratio of two to one reducing to one to one means that actually the ratio of surface area to volume is timesing by a half or dividing by two.

So we can see that, as we double the width, we quadruple the surface area.

We have an eightfold increase in volume, but the surface area to volume ratio halves.

So what I'd like you to do now is to calculate the surface area to volume ratio of cubes that have widths of seven, 14, and 28 millimetres.

And I'd like you to simplify those ratios to x to seven.

So if you divide them down so that the volume has a value of seven, what does that leave the surface area? That's what I'd like you to leave the simplification in.

Once you've done that, I'd like you to say what happens with the surface areas, the volumes, and the ratios as the width doubles.

And you can compare the seven, the 14, and the 28 millimetre cubes to help you with that description.

Then I'd like you to consider the fact that actually a sphere might be considered a more appropriate fit for some cells rather than a cube.

Now, to calculate the surface area of a sphere, you do four pi r squared.

And to calculate the volume of a sphere, you do 4/3 pi r cubed.

So I'd like you to use those equations to show the surface area to volume ratio of a sphere with a radius of one centimetre.

So the radius is the width from the outer edge into the centre, as shown in the diagram on the right, and you can use the value 3.

14 as your value for pi.

So pause the video while you're having a go at these calculations and come back to me when you are ready.

Okay, let's check our work then.

So firstly I asked you to calculate the surface area to volume ratio of cubes of seven, 14, and 28 millimetres wide.

So let's start with seven millimetres.

So for seven millimetres, the surface area, which is width times height times the number of faces, is seven times seven times six, which is 294 millimetres squared.

To calculate the volume we're timesing the width by height by depth, so that is seven times seven times seven, which equals 343 millimetres cubed.

And the surface area to volume ratio is therefore 294 to 343, which if simplified down to something to seven makes a ratio of six to seven.

What about then for the 14 millimetre cube? Well, for surface area it's 14 times 14 times six, which gives us a value of 1176 millimetres squared.

And for volume it's 14 times 14 times 14, which gives us a value of 2744 millimetres cubed.

So the surface area to volume ratio is 1176 to 2744.

And that simplified down to a ratio of seven is three to seven.

Then finally for the 28 millimetre cube, the surface area is 28 times 28 times six, which gives us a value of 4704 millimetre squared.

And volume is 28 times 28 times 28, and that gives us a value of 21,952 millimetres cubed.

So the surface area to volume ratio is 4704 to 21,952, which simplified down to something to seven gives us a value of 1.

5 to seven.

So did you get all of those correct? Just check over your work quickly to make sure that you did.

And well done.

So now let's look at the trends in surface area and volumes.

So we've seen the values that we got for surface area, volume, and surface area to volume ratio for seven, 14, and 28 millimetres cubed.

So let's see the trends.

So when we're going from seven to 14, and 14 to 28, we're at in each case doubling the width.

Now, when we're doubling the width, we can see that we're timesing by four, so we're quadrupling the surface area.

And that's true for both cases.

They're both a quadrupling of surface area.

But what about the volume? So the volume is increasing by eight times on both occasions.

Both are an eightfold increase.

And what about surface area to volume ratio? Well, we can see that they're both multiplying by naught 0.

5.

In other words, the surface area to volume ratio is halving.

So we can describe that in words to say that, as the width doubles, the surface area quadruples, volume increases eightfold and surface area to volume ratio halves.

So did you get all of those analysis correct? Well done if you did.

Then finally, I asked you to calculate the surface area to volume ratio of a sphere with a radius of one centimetre.

So let's see these calculations.

So for surface area we're doing four pi r squared.

So that means four times 3.

14 times one squared.

And that gives us a value of 12.

56 centimetres squared.

Now, to calculate volume, we need to use the equation 4/3 pi r cubed.

So to do that, we do four divided by three times 3.

14 times one cubed.

And that gives us a value of 4.

19 centimetres cubed.

So that means that our surface area to volume ratio is 12.

56 to 4.

19, which is more or less simplified to three to one.

So just check again your workings and make sure you've got your answers correct.

And well done again for doing that.

So there's some very obvious trends going on when we're increasing width, especially with cubes, and that's what we're going to explore next.

So and now we're going to have a look at the rate of diffusion in cubes.

Now the surface area of the cube affects the diffusion rate, and the volume of the cube affects the distance over which diffusion has to occur.

So both surface area and volume will impact diffusion.

Now, it's possible to see the effects of both the surface area and the volume on diffusion by observing the rate of diffusion of an acid through cubes of agar jelly.

And if those cubes are of different sizes, then we've got three here in the picture of one centimetre, one and a half centimetres, and two centimetres.

Then we will see a difference in the rate of diffusion into the centre of these cubes.

So what I'd like you to do is just to watch this experiment video to observe diffusion of an acid in a single cube of agar jelly so you've got a rough idea of what you are looking for.

(no audio) (no audio) (no audio) (no audio) (no audio) (no audio) (no audio) (no audio) (no audio) (no audio) (no audio) (no audio) (no audio) (no audio) (no audio) Okay, so we've seen that, in that example, the one centimetre agar cube completely discoloured in about 15 minutes.

So it took about 15 minutes for the liquid to diffuse half a centimetre, which is half the width of the cube.

15 minutes.

That's quite a long time, isn't it? Now, we could predict how long it would take for a two centimetre wide cube to fully discolour.

So what do you think? How long is that going to take? It took 15 minutes for a one centimetre cube to fully discolour.

So what do you reckon it would take, how long do you think it will take for a two centimetre wide cube to fully discolour? Now, we can observe those discolorations in the one centimetre, the one and a half centimetre, and the two centimetre wide agar cubes.

How long do you think each one will take to discolour? So make your predictions before playing the video.

(no audio) (no audio) (no audio) (no audio) (no audio) (no audio) (no audio) (no audio) (no audio) (no audio) (no audio) (no audio) So in that experiment we saw that the one centimetre cube fully discoloured in about 15 minutes, and the two centimetre cube fully discoloured in about 30 minutes.

Did you get it right? Did you make your prediction accurately? Well done if you did.

So we can see that by doubling the width we've approximately doubled the time it takes to diffuse to the centre.

So here's another trend that we're observing in our data.

So why is that the case, though? As the volume increases, we know that the surface area is increasing as well.

So why does the time taken increase as well? So let's look at those numbers again.

We've got a width of times two, a surface area increase of times four, a volume increase of times eight, but a surface area to volume ratio of times half.

So now that means that there is four times the surface area, but eight times the volume in the larger cube.

In other words, twice as much volume through which the substance has to diffuse.

And you can see that perhaps in the little squares drawn on the cubes on the diagrams. There's just much further, much greater volume through which diffusion has to pass.

And therefore, because it is twice the volume, it's going to take twice as long.

And that is why the time doubles.

Now, if we go back to our model bacterium, we can compare our model bacterium to the agar jelly cubes that we've just been investigating.

So if the bacterium was two centimetres wide and it took about 30 minutes to diffuse nutrients to the centre, do you think it would survive? Hmm, it probably would not.

No, because 30 minutes is a very long time to wait for nutrients to get from the outer part of your body, well, from the outside actually, right into the centre of your cell.

So what can we do about that then? Well, we could increase surface area without losing volume.

And we can do that by cutting the large cube up into smaller cubes, which would expose more surface area and therefore increase the rate of diffusion, reduce the length of time it takes four substances to diffuse into the centre of each of the smaller cubes.

So what I'd like you to do is just to summarise our conclusions so far using these bullet points and the words "increases" or "decreases," and only those two.

So as width increases, what happens to surface area, volume, surface area to volume ratio, and the time taken to diffuse into the centre.

So I'm going to give you five seconds to think about it.

Okay.

Let's see then.

So as width increases, surface area increases, volume increases, surface area to volume ratio decreases, and the time taken to diffuse into the centre of the cube increases.

Did you get all of those correct? Well done if you did.

So what I'd like you to do now is to consider these two questions.

Firstly, a two centimetre wide cube takes about 30 minutes to fully discolour.

If we cut a two centimetre wide cube into eight times one centimetre wide cubes, I would like you to suggest how long it would take the cubes to fully discolour.

And then I would like you to explain why that is the case.

Then I would like you to suggest why an organism which does not have any mechanisms for reducing the diffusion distance, in other words, they're not chopped up into small pieces, will not be able to grow very large.

And I'd like you to use the ideas of diffusion distance and time taken to diffuse to help you write your response.

So pause the video now and come back to me when you are ready.

Okay.

Let's see what you've written.

So the two centimetre wide cube takes about 30 minutes.

How long would it take for each cube if we chopped those into eight times one centimetre wide cubes instead? So how long would it take? Well, they would all discover in about half the time, and half the time is 15 minutes.

Why? So you might have said for this that this is because there is a larger surface area to volume ratio.

And after cutting, the equivalent area of surface has half the volume to serve in each small cube compared to the original large cube.

And therefore, diffusion to the centre will take half the time.

Now, you may have phrased that slightly differently, but have you got the right gist of what we're trying to say here? Make sure your explanation is clear, though, however you phrased it.

And well done for having a go, 'cause this is actually a really difficult thing to try and explain.

Then I asked you to suggest why an organism which does not have any mechanism for reducing the diffusion distance will not be able to grow very large.

So your answer might have said that the diffusion distance will increase as the size of the organism increases.

And the time taken for diffusion into the centre of the organism will double as the width doubles.

And therefore, at some point, the time taken for diffusion will be just too long and the organism will not survive at any greater size.

So again, check your work over.

Have you got those salient points? Again, you might well have phrased it differently, but make sure your meaning is clear and accurate.

Well done again.

That's really quite tricky thing to try and explain.

So well done if you've even got some of that right.

That is hard.

So in our lesson today we have seen that surface area and volume of cubes can be calculated and then compared as a ratio.

And we've seen that as the cube width doubles, so the surface area quadruples and the volume increases eightfold.

And we've also seen that we can observe the rate of diffusion using agar jelly cubes.

That's actually quite pretty to watch.

And as the width of the cubes doubles, the time taken for the substances to diffuse into the centre also doubles.

So in biological organisms, increasing the volume without significantly increasing the surface area really does limit the viability of the organism, because the time taken for substances to diffuse over the large distances will eventually become just unmanageable and unviable.

So I hope you've enjoyed our lesson today.

Well done for having a really good go at all those calculations and really tricky explanations.

And thank you very much for joining me.

I hope to see you again soon.

Bye.