Cell Area and Volume

size comparisons log scale

Show all your work, units and calculations.

1. Calculate the surface area, volume and the ratio of surface area to volume for a bacterium. Assume the bacterium is a cube 1 µm on a side.

surface area volume surface area / volume

 
 

 

 

 
 
 

2. Calculate the surface area, volume and the ratio of surface area to volume for a human cell. Assume the cell is a cube 10 µm on a side.

surface area volume surface area / volume

 
 

 

 

 
 
 

3. Contrast the surface area of the eukaryotic cell to the total surface area of all the bacteria in a colony that would have the same volume as the eukaryotic cell.
 
 
 
 
 

4. As cells increase in size the cell volume increases as the cube of the length (length3). Each unit of cell volume has nutrient and respiration gas requirements. The surface area will increase as the square (length2). All the cell's nutrients and respiration gases must travel through the cell surface. Discuss why this sets a limit to the maximum size of a cell.