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Year 9 iGCSE - Biology

Surface area to volume ratio can be a tricky concept to understand, however its the main reason why all animals on the earth are  made the way they are.

Surface area  to volume ratio

Lets first break it down into its components.

Firstly, what is Surface area (SA)?

The surface area of an object is the amount of surface that the object exposes to the outside. Your surface area is all of your skin.
We can calculate the SA of a cube using the following equation:

Length x Height x Number of sides

Lets calculate the SA of the cube to the left.

Length x Height x Number of sides = SA

1 x 1 x 6  = 6

This cube has a surface area of 6.

1 cm

1 cm

1 cm

The next step in surface area to volume ratio is calculating volume.

The Volume (V) is the amount of space that a substance or object occupies, or that is enclosed within a container.

So how much space you take up is your volume.

This is calculated by

Length x Height x Width

Lets use the same cube as before.

Length x Height x Width = V

1 x  1 x  1 = 1

In this case the cubes volume is 1

The final step is working out the Surface Area to Volume ratio.

SA / V

We’ll use the cube above for this example.

SA = 6

V = 1

6/1 = 6

The surface area to Volume ratio of this cube is 6.

Quick Questions.

1. What is surface area?

2. What is Volume and how do we calculate it?

3. Work out the SA:V ratio for the following cubes.

a.                         b.                            c.                              d.

2 2 2 7 7 7 12 12 12 18 18 18 1 cm

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In the above 4 examples what do you see, in terms of SA:V ratio?

You should notice the ratio getting smaller as the cube becomes larger and larger.

A 1 x 1 x 1 cube will have a SA:V of 6, while a 4 x 4 x 4 cube will have a SA:V of 1.5

This means an Elephant has a smaller SA:V than a mouse.

SA:V ratio is incredibly important. The greater your surface area to volume ratio the quick you can diffuse nutrient and heat.

This is why you often see little animals constantly shivering. Since they have a high SA:V they lose a lot of heat.

Here’s the main question.

Why do we have over 1,000,000 small cells instead of 5 larger cells?

What has more surface area. Sugar powder or sugar cubes?

Before your watch the two videos, make a hypothesis and explain your predication. Which react first and why?

Diffusion is only effective if the distance the particles have to travel is small and the organisms has a large SA:V.

Right now you may be thinking, elephants are huge and so are we, compared to a rat, but we survive just fine. This is because we are incredibly compact.

Lets look at our digestive system. Lining your small intestine are 1,000 of tiny structures called villi. These tiny villi are folds within the wall of the small intestine.

Digested food molecules are absorbed into the blood stream here. Vitamins, proteins, lipids and carbohydrates are all absorbed here.

In lungs, we increase the surface area by using tiny structures called Alveoli.

Millions of tiny little air sacs fill the lungs. These alveoli are only 1 cell thick and allow for maximum diffusion of gases.

A sufficient blood flow keeps the concentration gradient high, thin walls and a large surface area allow for easy diffusion.

Fish don’t have lungs like you and me, instead they have Gills. These gills are specially designed to extract oxygen from water.

Gills are composed of 1,000 of tiny filaments. These filaments are covered in Lamellae. These are small structures only 2 cells thick which are wrapped in capillaries.

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1 cm

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Quick Questions

1. How does having a large surface area to volume ratio help an animal survive?

2. Define Diffusion

3. What are 3 way diffusion can be increased in the human body


1. Explain how Villi and Alveoli work in the body

2. How do gills help a fish breath underwater?

3. Complete the table below to calculate the surface area to volume ratio of different sized cubes where L is the length of each side of a cube.

4. Draw a graph using the data above to compare the side length of a cube to its surface area to volume ratio.

5. Describe the relationship between the 2 variables

6. Observe the image to the right. Using the image explain why surface area to volume ratio is important to organisms.

(6 marks)

7. Explain why polar bears are large and thick, while the desert Coyote is thin and skinny. (4 marks)