AP Biology 2.2 Cell Size- Exam Style questions - FRQ
Question
A student conducts an experiment to investigate which cell shape would allow for the most efficient exchange of materials with its environment. Agar blocks (containing bromothymol blue dye) are cut into three different shapes to model three differently shaped cells. The agar blocks are then placed in a vinegar solution. As the vinegar diffuses into the agar models, the acid in the vinegar will turn the bromothymol blue dye yellow. The time required for each agar model to turn completely yellow is measured and is an indication of the efficiency of movement of materials into the agar models. The shape, volume, and surface area of each agar block is shown in the table.
| Shape | Volume | Surface Area |
| Cylinder | 25.1 \(cm^3\) | 50.2 \(cm^2\) |
| Sphere | 33.5 \(cm^3\) | 50.2 \(cm^2\) |
| Cube | 8 \(cm^3\) | 24 \(cm^2\) |
(a) Describe the measurement that would best predict the efficiency of each agar block’s exchange of materials with its environment. Calculate that measurement for each agar block.
(b) Identify the independent variable and the dependent variable in this experiment.
(c) Predict which cell would turn completely yellow first.
(d) Justify your prediction from part (c).
▶️Answer/Explanation
Ans:
(a) The measurement that would best predict the efficiency of each agar block’s exchange of materials with its environment is the surface area to volume ratio. For the cylinder, the ratio is \(\frac{50.2}{25.1}=2\). For the sphere, the ratio is \(\frac{50.2}{33.5}=1.5\). For the cube, the ratio is \(\frac{24}{8}=3\).
(b) The independent variable is the shape of the agar block. The dependent variable is the time it takes for the vinegar to diffuse completely into the cell and turn it yellow.
(c) The cube would turn completely yellow first.
(d) The greater a cell’s surface area to volume ratio, the more efficiently it will exchange materials with its environment. Since the cube has the greatest surface area to volume ratio, it will exchange materials the most efficiently and turn completely yellow first.