Why are cells so small?

Biggest cells

Surface area Area around the outside of the cell More surface area : more places for things to enter and exit cell. More surface area: healthier cell

Volume Volume = contents inside of the cell Healthier to have organelles are in need of raw materials. need to get rid of waste Healthier to have More surface area for each unit of volume

Smaller cells have a larger (better) surface area to volume ratio. 6 : 1 3 : 1 Surface area = 96 mm2 Volume = 64 mm3 1.5 : 1

Why are cells small? Materials move through cells by diffusion. small cells have: Larger surface area to volume ratio. More places on membrane for materials to move in and out for each unit of cytoplasm.

Ratio of Surface Area to Volume in Cells Cell Size Surface Area (length x height x 6) Volume (length x width x height) Ratio of Surface Area to Volume Go to Section:

Ratio of Surface Area to Volume in Cells Cell Size Surface Area (length x height x 6) Volume (length x width x height) Ratio of Surface Area to Volume Go to Section:

Ratio of Surface Area to Volume in Cells Cell Size Surface Area (length x height x 6) Volume (length x width x height) Ratio of Surface Area to Volume Go to Section:

Ratio of Surface Area to Volume in Cells Cell Size Surface Area (length x height x 6) Volume (length x width x height) Ratio of Surface Area to Volume Go to Section:

Ratio of Surface Area to Volume in Cells Cell Size Surface Area (length x height x 6) Volume (length x width x height) Ratio of Surface Area to Volume Go to Section:

Ratio of Surface Area to Volume in Cells Cell Size Surface Area (length x height x 6) Volume (length x width x height) Ratio of Surface Area to Volume Go to Section:

Ratio of Surface Area to Volume in Cells Cell Size Surface Area (length x height x 6) Volume (length x width x height) Ratio of Surface Area to Volume Go to Section:

Ratio of Surface Area to Volume in Cells Cell Size Surface Area (length x height x 6) Volume (length x width x height) Ratio of Surface Area to Volume Go to Section:

Ratio of Surface Area to Volume in Cells Cell Size Surface Area (length x height x 6) Volume (length x width x height) Ratio of Surface Area to Volume Go to Section:

Ratio of Surface Area to Volume in Cells Cell Size Surface Area (length x height x 6) Volume (length x width x height) Ratio of Surface Area to Volume Go to Section:

??? Questions to consider??? Which of the three cubes have the smallest surface area to volume ratio? Cell Size Surface Area (length x height x 6) Volume (length x width x height) Ratio of Surface Area to Volume

??? Questions to consider??? Which of the three cubes have the largest surface area to volume ratio? Cell Size Surface Area (length x height x 6) Volume (length x width x height) Ratio of Surface Area to Volume

??? Questions to consider??? In general, what happens to the ratio of surface area to volume as a cell grows? Cell Size Surface Area (length x height x 6) Volume (length x width x height) Ratio of Surface Area to Volume

??? Questions to consider??? Which ‘cell’ would be best able to take care of its needs? Why? Hint: Larger surface area to volume ratio gives more places on membrane for materials to move in and out for each unit of cytoplasm. Cell Size Surface Area (length x height x 6) Volume (length x width x height) Ratio of Surface Area to Volume

??? Questions to consider??? So…What does this have to do with cells being so small? Stay tuned for the story of Joe Cell……..

Cell Size Pencil Paper Lab Packet pages 3- 5 Joe Cell’s life Cell Size Pencil Paper Lab Packet pages 3- 5

Here is Joe Cell Joe started life as a happy, healthy, normal baby. Now that he has reached his teens, he’s begun to grow and grow and GROW! So far, he’s been okay, but he’s worried what job he’ll be able to get after high school if he’s a giant cell; after all, there’s no professional wrestling for cells! Let’s take a look at Joe’s growth and see if we can make some predictions about what’s in store for Joe’s future.

1. First, we need to measure Joe. A simple way to do this is to squish him into a box so he’s the shape of a perfect cube. (Joe won’t mind, he’s a flexible guy.) For example, Joe’s measurements at birth were a perfect 1u x 1u x 1 u. (a u is a micrometer, one millionth of a meter) Remember: Surface Area (SA) = L x W x 6 Volume (V) = L x W x H

Table, page 5 u x u x u Vol. x 5 mL SA x 10 mL SA = L x W x 6 Life Stage Measurements u x u x u Surface Area of a cube-shaped cell SA = L x W x 6 Volume Vol = L x H x W Joe Needs: Vol. x 5 mL Joe can get: SA x 10 mL Birth   1 x 1 x 1 Toddler

a. What was Joe’s surface area? In other words, how much cell membrane did he have exposed to the outside world?

Table, page 5 u x u x u Vol. x 5 mL SA = L x W x 6 SA x 10 mL Life Stage Measurements u x u x u Surface Area of a cube-shaped cell SA = L x W x 6 Volume Vol = L x H x W Joe Needs: Vol. x 5 mL Joe can get: SA x 10 mL Birth   1 x 1 x 1 1 x 1 x 6= 6 u2 Toddler

b. What was Joe’s volume? In other words, how much space did he have inside him?

Table, page 5 u x u x u Vol. x 5 mL SA = L x W x 6 SA x 10 mL Life Stage Measurements u x u x u Surface Area of a cube-shaped cell SA = L x W x 6 Volume Vol = L x H x W Joe Needs: Vol. x 5 mL Joe can get: SA x 10 mL Birth   1 x 1 x 1 1 x 1 x 6= 6 u2 1 x 1 x 1= 1u3 Toddler

Joe’s life story… Joe needs to get materials from the outside into him, and let the waste from his insides out. He has pores in his cell membrane. The larger the amount of cell membrane surface, the more materials can be exchanged.

How much food can Joe get? Materials can move through Joe’s membrane at a rate of 10 mL per day for every u2 of exposed surface area.

Table, page 5 u x u x u Vol. x 5 mL SA = L x W x 6 SA x 10 mL Life Stage Measurements u x u x u Surface Area of a cube-shaped cell SA = L x W x 6 Volume Vol = L x H x W Joe Needs: Vol. x 5 mL Joe can get: SA x 10 mL Birth   1 x 1 x 1 1 x 1 x 6= 6 u2 1 x 1 x 1= 1u3 Toddler

How much does Joe need? To keep Joe alive, he needs a total of 5 mL per day for every u3 of cell volume. These rates are genetically determined and will not change throughout Joe’s life

Table, page 5 u x u x u Vol. x 5 mL SA = L x W x 6 SA x 10 mL Life Stage Measurements u x u x u Surface Area of a cube-shaped cell SA = L x W x 6 Volume Vol = L x H x W Joe Needs: Vol. x 5 mL Joe can get: SA x 10 mL Birth   1 x 1 x 1 1 x 1 x 6= 6 u2 1 x 1 x 1= 1u3 Toddler

Joe’s problem C. Since Joe started life measuring 1u x 1u x 1u, was he able to get enough materials in and out to keep his insides functioning properly to sustain his life? Let’s do the math…..

What does Joe need? u x u x u Vol. x 5 mL SA = L x W x 6 SA x 10 mL Life Stage Measurements u x u x u Surface Area of a cube-shaped cell SA = L x W x 6 Volume Vol = L x H x W Joe Needs: Vol. x 5 mL Joe can get: SA x 10 mL Birth   1 x 1 x 1 1 x 1 x 6= 6 u2 1 x 1 x 1= 1u3 1 x 5 = 5 mL Toddler

What can Joe get? page 5 u x u x u Vol. x 5 mL SA = L x W x 6 Life Stage Measurements u x u x u Surface Area of a cube-shaped cell SA = L x W x 6 Volume Vol = L x H x W Joe Needs: Vol. x 5 mL Joe can get: SA x 10 mL Birth   1 x 1 x 1 1 x 1 x 6= 6 u2 1 x 1 x 1= 1u3 1 x 5 = 5 mL 6 x 10 = 60mL Toddler

Birth Joe needs 5 mL, he can get 60 mL. Joe’s OK!

Next time Joe’s parents took him to the doctor as a toddler, he measured 2u x 2u x 2u. A. What is his new surface area?

Table, page 5 u x u x u Vol. x 5 mL SA = L x W x 6 SA x 10 mL Life Stage Measurements u x u x u Surface Area of a cube-shaped cell SA = L x W x 6 Volume Vol = L x H x W Joe Needs: Vol. x 5 mL Joe can get: SA x 10 mL Birth   1 x 1 x 1 1 x 1 x 6= 6 u2 1 x 1 x 1= 1u3 1 x 5 = 5 mL 6 x 10 = 60mL Toddler 2 x 2 x 2

Table, page 5 u x u x u Vol. x 5 mL SA = L x W x 6 SA x 10 mL Life Stage Measurements u x u x u Surface Area of a cube-shaped cell SA = L x W x 6 Volume Vol = L x H x W Joe Needs: Vol. x 5 mL Joe can get: SA x 10 mL Birth   1 x 1 x 1 1 x 1 x 6= 6 u2 1 x 1 x 1= 1u3 1 x 5 = 5 mL 6 x 10 = 60mL Toddler 2 x 2 x 2 2 x 2 x 6 = 24 u2

2b. Will he be able to exchange enough materials to stay alive? What is his new volume? What does he need? What can he get?

New volume? page 5 u x u x u Vol. x 5 mL SA = L x W x 6 SA x 10 mL Life Stage Measurements u x u x u Surface Area of a cube-shaped cell SA = L x W x 6 Volume Vol = L x H x W Joe Needs: Vol. x 5 mL Joe can get: SA x 10 mL Birth   1 x 1 x 1 1 x 1 x 6= 6 u2 1 x 1 x 1= 1u3 1 x 5 = 5 mL 6 x 10 = 60mL Toddler 2 x 2 x 2 2 x 2 x 6 = 24 u2 2 x 2 x 2 = 8 u3

What does Joe need? u x u x u Vol. x 5 mL SA = L x W x 6 SA x 10 mL Life Stage Measurements u x u x u Surface Area of a cube-shaped cell SA = L x W x 6 Volume Vol = L x H x W Joe Needs: Vol. x 5 mL Joe can get: SA x 10 mL Birth   1 x 1 x 1 1 x 1 x 6= 6 u2 1 x 1 x 1= 1u3 1 x 5 = 5 mL 6 x 10 = 60mL Toddler 2 x 2 x 2 2 x 2 x 6 = 24 u2 2 x 2 x 2 = 8 u3 8 x 5 = 40 mL

What can Joe get? u x u x u Vol. x 5 mL SA = L x W x 6 SA x 10 mL Life Stage Measurements u x u x u Surface Area of a cube-shaped cell SA = L x W x 6 Volume Vol = L x H x W Joe Needs: Vol. x 5 mL Joe can get: SA x 10 mL Birth   1 x 1 x 1 1 x 1 x 6= 6 u2 1 x 1 x 1= 1u3 1 x 5 = 5 mL 6 x 10 = 60mL Toddler 2 x 2 x 2 2 x 2 x 6 = 24 u2 2 x 2 x 2 = 8 u3 8 x 5 = 40 mL 24 x 10 = 240 mL

Toddler Joe Joe needs 40 mL, he can get 240 mL. Joe’s OK!

Your Job: Continue answering the questions (pages 3-5) through Joe’s life as: A junior high student…. A junior in high school…. Joe today…. Is Joe going to be able to keep growing and still be OK? You need to find out! Show your math on the remaining part of the chart on page 5

Can Joe get what he needs? Homework: Finish the chart, answer the ?s Life Stage Measurements u x u x u Surface Area of a cube-shaped cell SA = L x W x 6 Volume Vol = L x H x W Joe Needs: Vol. x 5 mL Joe can get: SA x 10 mL Birth   1 x 1 x 1 1 x 1 x 6= 6 u2 1 x 1 x 1= 1u3 1 x 5 = 5 mL 6 x 10 = 60mL Toddler 2 x 2 x 2 2 x 2 x 6 = 24 u2 2 x 2 x 2 = 8 u3 8 x 5 = 40 mL 24 x 10 = 240 mL Junior High Junior in HS Present