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# The Sizes of Living Things

## Thinking about the Surface Area To Volume Ratio

Why are living organisms the sizes that they are?
Are there advantages to being large or small? What are the advantages to being a certain size?

When you make the outside of something bigger, interesting things happen to the inside. A little simple math can help us to see what happens. Then we will go on to dinosaurs and mice!

Let's look at some math examples.

Area

Here is a cube. Each edge measures two inches long.

How do we find the area of the surface, the outside?

We multiply two touching edges together.

Each edge is 2 inches long, so the area of one flat side of the cube is

2*2 = 4 square inches.

The area of one side of the cube is 4 square inches.

A cube has 6 sides.

4 square inches * 6 sides = 24 square inches.

So now we know the surface area of the outside of the whole cube.

Volume

Now let's think about the inside.

To find out the volume (how much is inside) of the cube we multiply height by width by length.

With this cube, we multiply 2*2*2 = 8 cubic inches.

So we have 24 square inches of surface to only 8 cubic inches of volume.

Is the surface always a larger number? Let's do some more cubes and see.

side of cube side*side Area of Side side*side*6 Area of Cube's Surface side*side*side Volume Ratio of Surface Area to Volume

2

2*2

4

2*2*6

24

2*2*2

8
3 to 1

4

4*4

16

4*4*6

96

4*4*4

64
3 to 2

6

6*6

36

6*6*6

216

6*6*6

216
3 to 3

8

8*8

64

8*8*6

384

8*8*8

512
3 to 4

12

12*12

144

12*12*6

864

12*12*12

1728
3 to 6

20

20*20

400

20*20*6

2400

20*20*20

8000
3 to 10

Let's look at the numbers here. I notice something very odd. When the inside of the cube (the volume) is small, the outside (the surface area) is large by comparison. What does this mean?

In practical terms for world builders, it means that small animals, like mice, have a lot of skin on the outside compared to a small volume of bones, blood, and internal organs on the inside. So a mouse or a baby bird looses heat rapidly.

When an animal has a large interior volume (big bones, muscles, lungs, digestive system) the skin on the outside (the surface area) gets progressively smaller when it is compared to the volume inside. This means that large animals tend to maintain their temperatures and to get cooler or warmer slowly.

Let's Apply These Ideas

Single-Celled Organisms

Why are single-celled organisms so small? Look at the table above. Tiny organisms have to take in food, water, gases, and chemicals, and they have to excrete waste products. They are full of organic molecules that have to be moved around and processed. In small cells, all parts of the cell are near the cell membrane, and chemical exchanges with the environment are simplified. As single cells grow larger, the contents increase in volume, and making everything work together becomes more complex. The cell wall, the interface between the living cell and the world, does not increase in area as quickly as the volume of the cell contents. At some point, the structures and processes in the cell will become inefficient if the cell becomes too large.

A sphere is a strong, efficient shape. Cells that are shaped like tiny bubbles contain the greatest volume for their surface area. However, cells come in a great variety of shapes. We have seen many cells that are shaped like tiny rods. Rod-shaped cells will have more surface area compared to their contents than spherical ones. However, as cells evolve to increase their surface area, they risk becoming increasingly fragile.

Small Animals

If you look at the table above, you can see that very small organisms have a lot of surface compared to their volumes. Small warm-blooded animals (endotherms), like mice and hummingbirds, have to eat a lot in proportion to their weights in order to keep themselves warm. In cold weather, a small animal loses heat rapidly because so much of it is in contact with the environment. It needs to eat a lot, stay in a warm area, and have good insulating fur or feathers.

On earth many small animals are cold-blooded (exothermic). Amphibians and fish, reptiles and insects, all deal with being small by metabolizing at the temperature of the environment. A small cold-blooded animal can warm up quickly on a sunlit rock, and requires little food to stay alive. This is certainly efficient. However, cold-blooded animals react more slowly than warm-blooded ones when they are cold. They need to find refuges safe from predators as the environment cools.

Large Animals

Being large also has consequences. Large animals can hold heat well, but may have trouble getting rid of body heat in very hot weather. This is an important problem, because proteins break down if the body gets too hot, and the organism may die if overheated. Many animals have developed ways of getting rid of extra heat by sweating or panting. Elephants can dissipate heat from their large, thin ears.

There is some disagreement about whether the dinosaurs were warm blooded or cold blooded, or in some intermediate stage. A large, warm dinosaur body could probably stay warm overnight, but if it ever got really chilled, it would take a very long time to warm it up!

Being large poses problems for supporting structures in the body. If you look at the table above you can see that if you double the measurements and then multiply the size by itself (this is called squaring the side, e.g., 6*6) you certainly get more surface area. However, when you multiply to get the volume you multiply side one by side two by side three, e.g., 6*6*6, which is called cubing the number. Therefore you get an important increase in volume, and weight. (We have used cubes for our example, but irregular shapes follow the same pattern of increase.) A larger animal needs more massive bones. More body cells need to be nourished: that means that the animal needs to have, and pump, more blood. It will need to enlarge lung size, and increase digestive capacity to get the extra food to support a larger body.

Animals adapt to their environments. Ponies are horses who have developed smaller bodies so that they can live where the pasture is sparse. The Science Series Nova has a program on the extinction of the mammoth. The last mammoths were pygmies, only three feet tall, living in an environment where there was not enough food to support their larger ancestors.