Surface Area to Volume Lab
Name:
6.0 Biology
Date:
Period:
INTRODUCTION:
Why are cells so small? Think about this: even though a whale is much larger than a human and a human is much larger
than a tulip, their cells are all roughly the same size. Whales do not have larger cells than humans, just more of them.
There is a very specific reason why cells are the size they are. Anytime this cell interacts with its environment, it does so
at its membrane. The more membrane a cell has, the more exchange it can perform with its environment. This exchange
can include activities such as obtaining nutrients or getting rid of wastes. We refer to the amount of surface that an object
has as its surface area (SA). How quickly exchange takes place depends on the surface area of the cell membrane. The
amount of food and oxygen needed and the amount of waste produced depends on the volume of the cell.
Once materials get inside the cell, they move via diffusion. Diffusion is the random movement of particles that results in
their dispersion in the cytoplasm. A drop of food coloring in a beaker of water will diffuse until the entire beaker is the
same color. This type of movement occurs inside cells as a way of dispersing molecules. Diffusion works best over short
distances. Imagine how long it would take food coloring molecules to diffuse in a water glass vs. in a swimming pool.
Because the water glass has less volume (V), diffusion is more efficient.
When cells grow to a certain size, their rate of growth slows down and then stops. They have reached their size
limit. When one of these larger cells divides into two smaller cells, the rate of growth again increases. In this investigation
you will experiment to determine why this is so.
Cells try to maximize their surface area (in order to improve exchange) and minimize their volume (to make diffusion
more efficient). A basketball-sized cell would have lots of surface area (good), but also lots of volume (bad). Think about
how long it would take molecules to diffuse from the outer portion of the ball to the center. A ping-pong ball or a marble
would be better choices. When we discuss the interplay of these two quantities, we use the ratio of surface area to volume
(abbreviated SA/V). Ideal cells have large SA values, but small V values.
EQUIPMENT AND MATERIALS:
test tubes
Agar with Bromothymol Blue (BTB) indicator
millimeter ruler
Vinegar – acetic acid
PROCEDURE:
1. Obtain a BTB agar block from your teacher.
2. With a spatula or knife, cut your agar into blocks with the following dimensions:
a. 1 cm x 1 cm x 1 cm
b. 1 cm x 1 cm x 4 cm
c. 2 cm x 2 cm x 2 cm
3. Record the measurements of each block.
4. Place the agar blocks in 3 large test tubes.
5. Measure 25 mL of vinegar using a graduated cylinder.
6. Submerge all of the agar blocks in the vinegar solution.
7. Allow the cubes to soak for 8 minutes.
8. Pour the vinegar down the sink and rinse the cubes with water. Use care that you do not pour your agar
cubes out of the test tube.
9. Remove the agar cubes and blot them dry with a paper towel.
10. With your spatula blade or knife, cut the agar cubes to remove a slice from the middle of the agar block.
11. Observe the depth of the yellow area around the edge of the agar slice. This is known as the amount of
absorption and should be recorded in the vinegar absorbed column.
12. Using your measurements, determine the surface area, volume, and surface area to volume ratio of each
block and record it on the data table.
Surface area (mm2) = L x W of each side, add the 6 numbers together
a is the length of the side of each edge of the cube
Surface area of a cube = 6 a2
a, b, and c are the lengths of the 3 sides
Surface Area of a Rectangular Prism = 2ab + 2bc + 2ac
Volume (mm3) = L x W x H
SA:V = Surface area to volume ratio = surface area / volume
DATA and CALCULATIONS TABLE
Cube Dimensions
(mm)
L, W, H
Surface Area
(mm2)
Volume
(mm3)
SA:V Ratio
Vinegar
Absorbed
(mm)
A
B
C
RESULTS – Draw your cubes to scale, and shade in the area that was blue and yellow. Use a ruler to draw
straight edges.
QUESTIONS:
1. Which cube has the greatest surface area?
2. Which cube has the greatest surface area to volume ratio?
3. What evidence is there that vinegar is being absorbed by the agar cubes?
4. Was the vinegar absorbed completely through any one of the cubes? If so, which cube? If not, which cube
absorbed the most vinegar? Explain why one cube would absorb more vinegar than another cube.
5. If the vinegar were some vital substance, such as food, and the agar cubes were cells, which cell would be
fed the most efficiently? Why?
6. What happens to the cell’s ability to absorb materials and get rid of waste as it increases in size?
7. Make a statement which explains why cells are limited in the size to which they can grow.
8. For cubes A, B and C calculate what percentage of the cube remained clear.