Determine the surface area of the cellular sphere. The formula for surface area of a sphere is given as: Surface Area = 4 * pi * r^2, where pi is the mathematical constant and r is the radius of the sphere.
Determine the volume of the cell. The formula for volume of a sphere is identified as: Volume = (4 * pi * r^3)/3.
Make a ratio of the two formulas, placing surface area on top.
Surface area--to--volume ratio = [4 * pi * r^2] / [(4 * pi * r^3)/3].
Understand the significance of the ratio. It can be seen that as the radius, r, of a sphere increases, the value for the volume will increase at a much faster rate than the surface area based on the respective exponential values. As the radius increases even more, the disparity between the two measurements will become greater, thus indicating a smaller surface--to--volume ratio. Essentially, the volume of the cell becomes too large for the movement of materials within the cell and also for the movement of materials across the cell membrane with its smaller surface area.