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Why are Cells so Small?
Cell Size and Surface Area to Volume Ratio
Name _______________________
Date ______________ Per _____
Learning Objectives:
 LO 2.6: The student is able to use calculated surface-to-volume ratios to predict which cell(s) might
eliminate wastes or procure nutrients faster by diffusion.
 LO 2.7: Students will be able to explain how cell size and shape affect the overall rat of nutrient intake and
the rate of waste elimination.
 LO 2.13: The student is able to explain how internal membranes and organelles contribute to cell functions.
Introduction:
All organisms are composed of cells. The size and shape of a cell determines how well it can deliver nutrients to its
interior. Since all cells and organisms depend upon the efficient delivery of gases, nutrients, and other important
molecules, the relationship between a cell's surface area and its volume is an important regulating concept.
Cells are limited in how large they can be. This is because the surface area and volume ratio does not stay the
same as their size increases. Because of this, it is harder for a large cell to pass materials in and out of the
membrane, and to move materials through the cell.
Exercise I:
In this part of the lab, you will make cube shaped models to represent cells. The dimension along one side will
be doubled with each model. You will then calculate the surface area, volume, and the ratio between the two.
The surface area and volume are calculated as shown in the figure below:
Questions:
1. List some of the things that cross a cell’s membrane.
a. ________________________ b. ________________________ c. ________________________
2. Why is it important that a cell have a large surface area relative to its volume? (In other words, a high
surface area to volume ratio.)
_________________________________________________________________________________
_________________________________________________________________________________
3. Cut out and construct the four cell models. Fold and tape into cubes with the tabs to the inside.
Measure and record the dimensions in the Table 1.
Table 1. Cell Size Comparison
Cube
(cell)
Dimensions (cm)
1
(smallest)
____ x ____ x ____
2
3
4
(largest)
Surface Area
(cm2)
Volume
(cm3)
Surface Area to Volume Ratio
4. Calculate the total surface areas, volumes, and surface area-to volume ratios for each cell model and
record it in table 1. Show calculations in the table.
5. Which model has the largest surface area? _______________________________________________
6. Which model has the largest volume? ___________________________________________________
7. Which model has the largest ratio? _____________________________________________________
8. What is happening to the surface area to volume ratio as the cell size increases?
_________________________________________________________________________________
_________________________________________________________________________________
Exercise 2:
In this exercise we will explore the impact of shape on surface to volume ratios. The four shapes given below
have approximately the same volume (1 mm3). Complete the calculations for each shape. To calculate the
volume of environment within 1.0 mm of the shape, imagine the shape surrounded by a larger shape of the
same size that is 1.0 mm bigger on all sides.
Table 2. The Effect of shape on surface area-to-volume ratios.
Shape
Dimensions
(mm)
Sphere
1.2 diameter
Cube
1x1x1
Filament
0.1 x 0.1 x 100
Column
1.2 diameter x 1
Volume (mm3)
Surface area
(mm2)
S/V ratio
Volume of
environment
within 1.0 mm
Questions:
1. Make a sketch, to scale, of the four objects.
2. Which shape has the largest surface area? _______________________________________________
3. Which shape has the largest volume? ___________________________________________________
Haut, J. (2014). Modified from “Limits to Size-Why are Cells so Small?” and “Sizes of Organisms: The Surface Area:Volume Ratio.”
4. Which shape has the largest ratio? _____________________________________________________
5. If you had to select a package with the greatest volume and smallest surface area, what shape would it
be? ______________________________________________________________________________
Lab Analysis:
1. To maintain life, and carry-out cellular functions, materials must be able to move into and out of the cell.
Also, material needs to be able to move within the cell. What might be the advantage of having a large
surface area?
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
2. Since transport of materials in and out of the cell can only happen at the cell’s surface, what problem
does this pose for larger cells?
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
3. Do larger organisms have larger cells than smaller organisms, or more cells than smaller organisms?
Explain.
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
4. What is the advantage of having folded membrane surrounding the cell (i.e. plasma membrane), or
within the cytoplasm (i.e. endoplasmic reticulum) or within organelles (i.e. chloroplast)?
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
_________________________________________________________________________________
Haut, J. (2014). Modified from “Limits to Size-Why are Cells so Small?” and “Sizes of Organisms: The Surface Area:Volume Ratio.”
Haut, J. (2014). Modified from “Limits to Size-Why are Cells so Small?” and “Sizes of Organisms: The Surface Area:Volume Ratio.”
Haut, J. (2014). Modified from “Limits to Size-Why are Cells so Small?” and “Sizes of Organisms: The Surface Area:Volume Ratio.”