Answer:
The speed of filling up with oxygen ( or any other gas, that is) is called the rate of diffusion. It depends on the temperature, distance and cell surface. Since from the diagram we can assume that the temperature and the distance between cell and oxygen is the same for both cells, then the only factor that affects the rate of diffusion is the cell's surface. Since the cells here are presented as cubes, the surface of the cube is 6 • a^2. So, the surface of the larger cell is 6 • 10^2, which is 600, and the second cell is 6 • 5^2, which is 150. That means that the larger cell will fill up with oxygen faster.
Regarding the amount of oxygen the cells can store, we need to calculate the volume of each cell. They are cubes, so the volume is a • a • a. So, the larger cell has a volume of 10 • 10 • 10, which is 1000 cubic microns, and the smaller one 5 • 5 • 5, which is 125 cubic microns.
The ability of smaller cells is to divide faster than the big ones, which is, let's say, a sort of compensatory mechanism for their lack of size. So, in order to hold more oxygen, smaller cells divide.
In the situation where we have 1 large and 8 smaller cells, to determine which will fill with oxygen faster, again we need to determine their surfaces. We already calculated large cell's surface, which is 600 square microns. The surface of one small cell was also calculated, and it is 150 square microns. If we have 8 cells, their surface is 8 • 150, which is 1200. That means that 8 smaller cells have a greater rate of diffusion.
Regarding their volume, we already calculated that a large cell's volume was 1000 cubic microns, and one small cell had a volume of 125. That means that 8 small cells will have a volume of 8 • 125, which is 1000 cubic microns. That means that one large and eight small cells have the same volume.
Finally, since 1 large and 8 small cells have the same volume, but smaller cells have the greater surface ( as calculated before), that is the reason why it is better to have more smaller than one large cell.
