Use the models that you created in lesson 2, lab 1 to you answer the following question.
compare the surface area to volume ratio of a large cell to that of a small cell
why does the ratio of surface area to volume increase with the decrease in cell size?

a. a smaller cell has an equal ratio of surface area to volume
b. a smaller cell has more surface area than volume.
c. a smaller cell has more volume than surface area
d. a larger cell has more surface area than volume

The answer is B. A smaller cell has more surface area than volume.

This is simple mathematics. Let's imagine that cell is spherical.
Now, we have two spheres: one big (with radius r = 5 cm) and one small (with radius r = 2 cm).
The formula for the surface area of the sphere (A) is A = 4 π r².
The formula for the volume of the square is 4/3 π r³.

Now, let's compare two spheres:

Small sphere:                                                  Big sphere:
r = 2 cm                                                            r = 5 cm
A = 4 π 2² = 50.3 cm²                                      A = 4 π 5² = 314.2 cm²
V = 4/3 π 2³ = 33.5 cm³                                   V = 4/3 π 5 ³ = 523.6 cm³ 

According to the calculation, the smaller sphere will have more surface area than volume. This can be extrapolated to all shapes, not only spheres, so the smaller cell has more surface area than volume.

A. mitochondrion b. nucleus