Welcome this is Mr. W and this video is about surface area to
volume ratios and how those ratios impact structure and function in living things.
In this video we're going to use one concept —surface area to volume ratio — to explain why
cells are small, why whales are big, why elephants have big ears, why flat worms have no special
system for moving oxygen into their cells, and why when you get cold you hold your arms against
your body. One concept to explain them all! Let's start with a demonstration. This block is made of
agar (a seaweed extract) a bit of the base sodium hydroxide, and a pH indicator. This pH indicator —
phenolphthalein —is this very nice fuchsia color when it's exposed to a base and it turns clear
when the pH turns acidic. I've cut cubes of this agar into four different sizes. The biggest is
3 centimeters on a side. The others are 2, 1, and 0.5 centimeters on a side. I'm going to put these
cubes into a dish of vinegar, a weak acid. Watch what happens. In 6 minutes the tiny cube has lost
its fuchsia color and turned completely white. The other cubes still have some fuchsia inside and the
percentage that's still fuchsia goes up with the size of each cube. In other words vinegar diffused
into 100% of the smallest cube's volume while it reached only 19% of the largest cube's volume.
Let's get our heads around what's really going on. Diffusion is the movement of molecules in a fluid,
a gas, or a liquid from where they're more concentrated or bunched up to where they're more
spread out. It's how this drop of food coloring is spreading throughout this flask. You don't
have to stir or add energy. The random movement of the food coloring molecules will lead them,
over time, to move apart from one another. When we put our agar cubes in the vinegar,
the vinegar is more concentrated outside the cubes that it is inside. So because there's nothing from
stopping the vinegar from moving in, the vinegar diffuses from where it is (outside the cubes)
where it isn't (inside the cubes). The vinegar is diffusing through the outer surface of each
cube and we can quantify the amount of surface by measuring the surface area of each cube. In
this table I'm going to list the surface area for each of the four cubes plus three imaginary ones:
one smaller (0.1 centimeters on a side) and two bigger (5 centimeters on a side and 10 centimeters
on a side). The vinegar is diffusing through the outer surface and into the cube's volume. The
smallest cube has the smallest volume at 0.001 centimeters cubed while the largest cube has
the largest volume 1000 centimeters cubed. What we're concerned with is the ratio of surface area
to volume. A ratio is the relationship between two numbers and the ratio we want is the ratio
between the surface area for each cube divided by its volume. So in our tiny imaginary cube,
0.1 centimeters on a side, the surface area to volume ratio is 60:1. In the largest cube that
we're considering, 10 centimeters on a side, the ratio is a hundred times less, 0.6:1. The smaller
a cube is, the larger its ratio of surface area to volume. And conversely the larger a cube is
the smaller its ratio of surface area to volume. In other words the larger something is the less
surface area it has relative to its volume. And that's why cells are small. Cells, to stay alive,
have to exchange materials with their environment. For most cells that means that things like oxygen
and food need to go in and carbon dioxide and other wastes need to come out. That exchange is
largely by diffusion. If cells were too big then diffusion wouldn't work in terms of reaching the
entire volume of the cell. Just pretend that the smallest agar cube was a cell and that the
vinegar molecules were oxygen. This cell is doing fine: oxygen is getting all the way, deep into the
cell. Things are diffusing in and out. This cell is well-adapted to exchange substances with its
environment through diffusion. But if these larger cubes were also cells they'd be having a hard
time. Whatever needs to get in isn't getting in very far. A lot of this poor cell would be
suffocating and filling up with waste that can't diffuse out. Tininess gives cells a very high
surface area to volume ratio and that's why cells are small. All right. So what's with the flat ears
on the elephants? Well, elephants are mammals just like we are. And like us they maintain
a constantly high body temperature. We mammals like [for] ourselves to be warm but too warm is
dangerous because excessive heat can reduce enzyme function by denaturing enzymes. That can kill you.
Because elephants are big their bodies have very little surface area relative to their enormous
volume and this makes it very difficult for heat to diffuse out of the elephant's body. So think
about this in terms of the long slow process of evolution. As the ancestors of elephants evolved
to grow bigger they needed other adaptations to improve their ability to allow heat to diffuse out
of their bodies. And that's what the elephant's huge ears do. In the thin flap of skin that makes
up each ear blood can circulate and the heat of that blood, being close to the surface,
can diffuse out of the elephant's body. That's the adaptation:a flat sheet of tissue that makes
heat diffusion easier. To simulate this, let's cut a flat sheet of our phenolphthalein agar and
put that in vinegar. Because it's flat this flat sheet has a very high surface area to volume ratio
so it's very easy for the vinegar to reach the entire volume of this sheet in a relatively short
time. Summary: big flat appendages with their high surface area to volume ratio are often adaptations
for radiating heat into the environment. And how about this flat worm? No heart. No lungs. How is
oxygen getting to all of its cells? How is carbon dioxide getting out? Because these animals are
flat they have a very high surface area to volume ratio. So you can assume that oxygen just diffuses
from the surrounding water in and carbon dioxide from the body cells out. And what about the huge
size of whales? For whales, who often live in cold water, the problem is the opposite of the problem
that elephants face. Elephants have to deal with overheating. Whales have to struggle with
hypothermia, with heat loss. So think about the fact that in water that's a nice 80 degrees (F) a
human being can become hypothermic within a couple of hours. How do whales survive lifelong immersion
in ocean water? Size is a big part of how whales adapted to the cold stress involved in living
in water. Whales are huge. Huge things, just by the math, have a very low surface area to volume
ratio. That means that the heat inside a whale's body is effectively trapped inside. There's no
way for it to get out. Remember our cubes? Large size is bad for diffusion. So just by evolving
large size whales decreased their surface area to volume ratio. This made it easier for them to
maintain their body temperature. It was selective advantage: genes for size got passed on because of
surface area to volume considerations. You know I'm filming this in the early winter and it just
got pretty cold here in California. Oh my goodness look at what I did. I'm holding my arms against
my body. By doing that I'm effectively decreasing my surface area while of course keeping my volume
the same. Holy cow that means that this is a behavioral adaptation for decreasing my surface
area to volume ratio, preventing diffusion of heat. And what about this? These ridges
of tissue are the villi of the small intestine. Their job: absorbing food from the gut into the
bloodstream. Why do you think they have this wavy shape? Because a wavy surface increases surface
area to volume ratios. To demonstrate this I cut a piece of agar to very roughly the shape of the
villi of the small intestine. All of these ridges have the effect of increasing the surface area to
volume ratio. As a result diffusion happens more easily and you can absorb the food that you need
to absorb from your gut into your blood. We've seen in this video how important surface area to
volume ratios are. How increasing the ratio of surface area to volume makes diffusion easier,
leading to adaptations like big ears in elephants or the flat shape of the
flatworm and wavy tissues. We've also seen how decreasing the ratio of surface area to volume
makes diffusion harder leading to adaptations like folded arms against our body or evolving to
great size if you're a whale. So thanks so much for joining me over at sciencemusicvideos.com
(now Learn-Biology.com) you'll be able to find an interactive tutorial about surface area and
volume. It's going to really help you solidify your understanding of this unbelievably powerful
concept. So head on over to sciencemusicvideos.com (now Learn-Biology.com) where you can study this
or dozens of other topics. I want to thank you for joining me. Again leave me comments,
leave me questions ,and I'll see you next time at our next video. Thanks!