Cells divide when they reach a certain size. The rate of the chemical reactions in the cytoplasm of cells (known as metabolism) is corresponding to the volume of the cell. It is necessary for the substances used in the reactions to be absorbed by the cell and wastes are thrown out, in order to keep the metabolism running. These substances move through the cells at the surface of the cells, thus the rate at which substances cross the plasma membrane depends on its surface area.
Surface area to volume ratio of a cell is important in these following ways:
- If the ratio is too small, waste products will increase since the substances can not enter the cell fast enough, which causes the wastes to be produced quicker than they are thrown out.
- If the ratio is too small, the cells can overheat due to the metabolism’s rapid production of heat than it’s lost on the cell’s surface.
*surface area of cell -> varies rate of materials leaving/entering cell
*volume of cell -> varies rate of materials used/produced
1) The surface area of: an Streptococcus pneumoniae is 4π(0.5)^2≈ 3.14 µm^2, an white blood cell is 4π(5µm)^2≈ 314.16 µm^2, and an egg cell is 4π(50)^2≈ 31415.93 µm^2.
2) The volume of: an Streptococcus pneumoniae is is 4/3π(0.5)^3≈ 0.52µm^3 ,an white blood cell is 4/3π(5µm)^3≈ 523.60 µm^3, and an egg cell is is 4/3π(50)^3≈ is 523, 598.78 µm^3.
3) The surface area to volume ratio of: an Streptococcus pneumoniae is 3.14/0.52≈ 6.04 , an white blood cell is 314.16/523.60=0.6, and an egg cell is 31415.93/523, 598.78≈ 0.06.
4) As the diameter increases, the surface area to the volume ratio of a sphere decreases. This evidence can be seen with the egg cell which has the largest diameter of 100µm and resulted with the smallest ratio of the surface area to the volume.
5) a) With a small size and a large surface are to volume ratio, the Streptococcus pneumoniae has an advantage by being able to have a faster metabolism with the substances moving quickly throughout the cell.
b) No human cells may not be larger than the egg cell because of the risk of a very slow metabolism and overheat of the cells. Although the egg cell has a very small ratio and a large diameter, it does not have to carry out much chemical reactions within itself. Thus, other cells which do need to perform greater chemical reactions and have a fast metabolism (in order to keep wastes from accumulating and overheating of the cell) will have to be much more smaller than the size of an egg cell.
Graphs help show relationships betweeen two variables and may display the results of an experiment. While the placement of points can show the relationship, drawing a line can help make the relationship more evident. Variables on the x-axis are known as the independent variables, which are variables that are not altered by any other variables. Dependent variables, or variables that are affected, are displayed on the y-axis.
*AA-CC: 14-5; DBQ p14 • AA-SG: 5