Introduction to Cell & Molecular Biology
(BIOL121) - Dr. S.G. Saupe (ssaupe@csbsju.edu); Biology Department, College of St. Benedict/St. John's
University, Collegeville, MN 56321 |

**Cell Unit: Bonus Assignment Answer**

__ The Problem__: Calculate the approximate
number of cells in a human body. Assume that a typical cell is 100
μm in diameter.

First you need to know the volume of a typical human. You could do this by measuring your body, and assuming you are made up of a sphere (head) and 5 cylinders (torso, legs, arms) calculate your volume from the equations below. Another way is to do some research to find the volume of a typical person which is presumably about 19 gallons (click here for a reference). Then convert this value to liters (= 71.9 liters)

If a typical cell has a diameter of 100
μm then its radius is 50
μm and its volume is 523625
μm^{3} (=4.189 x 50^{3}).

Now, we simply need to divide the volume of a person by the volume of one cell. But, we need to make sure that the units are the same. Thus:

71.9 liters523625
μm^{3} |
x |
1 �m^{3
} 10^{-15} L |
= | 137312007639 = 1.37 X
10^{11 }
cells |

= = = = = = = = = = = = = = = =

Volume of a cylinder = (p) r^{2}h

Volume of a
sphere = 4/3 (p) r^{3} = 4.189 r^{3 }

Metric Conversions

1 mm

^{3}= 1 �L = 1000 nL = 1 x 10^{-6}pL

1 cm^{3}= 1 mL

1 �m^{3}= 10^{-9}mm^{3}= 10^{-9}�L = 10^{-6}nL = 10^{-3}pL

1 �m^{3}= 10^{-15}L

Last updated: July 14, 2009 � Copyright by SG Saupe