
Find the total surface area of the cube:
 Side length (l)
 Surface area of one side = l x l = l2
 Total surface area = 6 x l2

Calculate the volume of the cube:
 Height (h) = l
 Volume = l2 x h

A ratio compares two numbers by dividing
one number by the other. It can be expressed
in three ways:

In words
As a fraction
With a colon


x to y
x/y
x:y

For the surface area-to-volume ratio, divide
total surface area by volume
Total surface area
volume

Side length (l) = 4mm

SA of one side: l2 = 4mm x 4mm = 16mm2

Total SA: 6 x l2 = 6 x 16mm2 = 96mm2

Total SA= 96mm2

Height (h) = l = 4mm

Volume = l2 x h = 16mm2 x 4mm = 64mm3

Volume = 64mm3
Total surface area
volume
=
96
64
Divide both numbers by their greatest common factor: (32)
(96 ÷ 32)
(64 ÷ 32)
=
3
2
3:2
3 to 2

Calculate the surface area-to-volume of a
cube with a side length of 3mm

l = 3mm

Total SA: 54mm2
Volume: 27mm3

(54 ÷ 9)
(27 ÷ 9) =
6
3
=
2
1 2:1
2 to 1
 Ok, so why do we bother to
know this?
 In biology, why do we do this?

How does the flatness of a single-celled
Paramecium, (like you saw in the pond H2O),
affect the cell’s surface area-to-volume ratio?

By being flat, a Paramecium spreads it
volume over a large area. The surface areato-volume ratio is increased because there is
more surface area per unit volume.

Are there limits to how large a cell can grow? Everything that
enters and exits a cell passes through the cell membrane.

As the size of a cell increases, its surface area increases, but so
does its volume.

Consider how people enter a crowded event at a large stadium.
Everyone funnels through a few gates. In a larger stadium, it
takes people longer to move in and out.

Similarly, in a larger cell, it takes materials longer to reach their
destination inside the cell. This means that it is more difficult
for a large cell to have its needs met through the cell
membrane.
SOL Test Example

In this lab, you will examine surface area-tovolume ratios on a small scale, using model
cells. You will use the collected data to draw
conclusions about why this ratio might limit
the size of a cell.

Cut out the cube diagrams and put together your “cell” model.
Use tape to hold it together

Use a ruler to measure the length, width, and height dimensions
of each model. (Round to the nearest whole #)

Record the dimensions in Table 1

Calculate the total surface area for each model. Enter the data in
Table 1

(We aren’t using sand!) Calculate the volume for each model and
record values in Table 1

Finally, calculate the surface area-to-volume ratio and enter it into
Table 1