1 of 9

© Getting Down with Science

2 of 9

Cell Size

Cellular metabolism depends on cell size

Cellular waste must leave

Nutrients and other resources/chemical materials must enter

At a certain size, it begins to be too difficult for a cell to regulate what comes in and what goes out of the plasma membrane

Dissipate thermal energy

© Getting Down with Science

3 of 9

Surface Area and Volume

The size of a cell will dictate the function

  • Cells need a high surface area-to-volume ratio to optimize the exchange of material through the plasma membrane

​

© Getting Down with Science

4 of 9

Formulas

  • Formulas for cuboidal cells
    • Total SA= height x width x number of sides x number of boxes (or SA = 6S2 if only 1 box)
    • Total V= height x width x length x number of boxes (or V = S3 if only one box)
    • SA to V ratio = SA/V
  • Formulas for spherical cells
    • SA = 4πr2
    • V = 4/3πr3
    • SA:V ratio = SA/V

​

Remember: all formulas are given to you on the AP exam

© Getting Down with Science

5 of 9

Practice

SA = 3 x 3 x 6 x 1 = 54 units2

V= 3 x 3 x 3 x 1 = 27 units3

SA:V = 54/27 = 2

SA = 1 x 1 x 6 x 27 = 162 units2

V= 1 x 1 x 1 x 27 = 27 units3

SA:V = 162/27 = 6

#1

#2

Which would have the best exchange of material through the plasma membrane?

Example: cuboidal cell

Option 2: SA:V ratio is higher

© Getting Down with Science

6 of 9

Practice

How does the radius affect the SA:V ratio in spherical cells?

SA = 4πr2

V =4/3πr3

SA:V ratio = SA/V

SA

V

4πr2

πr3

4

3

r

3

r

As r increases, the ratio of SA:V decreases

1

1

3

© Getting Down with Science

7 of 9

Try it

SA = 4 x π x 52 = 314 units2

V= 4/3 x π x 53 = 523.3 units3

SA:V = 314/523.3 = 0.6

SA = 4 x π x 82 = 803.8 units2

V= 4/3 x π x 83 = 2143.6 units3

SA:V = 803.8/ 2143.6 = 0.37

​

#1

#2

Which would have the best exchange of material through the plasma membrane?

Example: spherical cell

Option 1: SA:V ratio is higher

Complete practice problems 1-3 on packet p. 18

​

r=5

r=8

© Getting Down with Science

8 of 9

What Does This Mean for a Cell?

Cells tend to be small

  • Small cells have a high SA:V ratio
    • Optimizes exchange of materials at the plasma membrane
  • Larger cells have a lower SA:V ratio
    • Lose efficiency exchanging materials
      • The cellular demand for resources increases
      • Rate of heat exchange decreases

© Getting Down with Science

9 of 9

Practice Problems & Agar Lab

Let’s see cell size in reality. See lab sheet and follow directions. You need a calculator and pencil.

​

Complete practice problems 4-12 during “down time” in lab today.

​

Lab due today!

© Getting Down with Science