Question

surface area to volume ratio
the surface area of a cell is defined as the amount of surface covering the outer part of the cell. the volume of a cell is the amount of space the entire cell takes up. by comparing a cells surface area to volume ratio, we can figure out how efficient a cell is at transporting materials in and out. the larger the ratio, the more efficient the cell is.
using some simple calculations, we can calculate the surface area to volume ratio of different sized cells. (note, most cells are not shaped like cubes, but we will use cubes to simplify the math).
formula for surface area of a cube: length x width x number of sides
formula for volume of a cube: length x width x height
calculate the surface area and volume of the three beet cubes you have soaking in the bleach. to find the sa:v ratio, simplify the numbers by finding the greatest common factor. use the example below as a guide.

length of sides	surface area	volume	sa : v ratio
2 cm
1 cm
0.5 cm

checkpoint #2:
d. smaller cells are more / less (circle one) efficient than larger cells.
e. which size beet cube had the largest surface area to volume ratio?
back to the lab!

1. after 30 minutes have passed, use a spoon and remove the cubes from the beaker and place them on the paper plate. dab off any excess bleach with a paper towel.
2. using a knife, slice the beet cubes in half. observe any color changes and sketch what you see in the diagram below.
3. using a ruler, measure the diameter of the remaining red pigment and record in the table below. be sure to include units on your measurements.

cube size	diameter of red pigment
1 cm
0.5 cm

Explanation:

Step1: Recall surface - area formula for cube

For a cube with side length $s$, surface area $SA = 6s^{2}$ (since length = width = height = $s$ and number of sides = 6).

Step2: Recall volume formula for cube

Volume $V=s^{3}$.

Step3: Calculate for $s = 2$ cm

$SA=6\times(2)^{2}=6\times4 = 24$ $cm^{2}$, $V=(2)^{3}=8$ $cm^{3}$, $SA:V=\frac{24}{8}=\frac{3}{1}=3:1$.

Step4: Calculate for $s = 1$ cm

$SA=6\times(1)^{2}=6$ $cm^{2}$, $V=(1)^{3}=1$ $cm^{3}$, $SA:V=\frac{6}{1}=6:1$.

Step5: Calculate for $s = 0.5$ cm

$SA=6\times(0.5)^{2}=6\times0.25 = 1.5$ $cm^{2}$, $V=(0.5)^{3}=0.125$ $cm^{3}$, $SA:V=\frac{1.5}{0.125}=\frac{1.5\times8}{0.125\times8}=\frac{12}{1}=12:1$.

Step6: Answer checkpoint d

Smaller cells have a larger surface - area to volume ratio. Since a larger ratio means more efficient transport, smaller cells are MORE efficient than larger cells.

Step7: Answer checkpoint e

The $0.5$ cm size beet cube had the largest surface - area to volume ratio.

Answer:

Length of Sides	Surface Area	Volume	SA : V ratio
1 cm	6 $cm^{2}$	1 $cm^{3}$	6:1
0.5 cm	1.5 $cm^{2}$	0.125 $cm^{3}$	12:1

d. MORE
e. 0.5 cm