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

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 μm3 (=4.189 x 503).

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 liters 523625 μm3 x 1      �m3 10-15  L = 137312007639 = 1.37 X 1011  cells

= = = = = = = = = = = = = = = =
Volume of a cylinder = (p) r2h
Volume of a sphere = 4/3 (p) r3 = 4.189 r3

Metric Conversions

1 mm3 = 1 �L  =  1000 nL = 1 x 10-6 pL
1 cm3 = 1 mL
1 �m3 = 10-9 mm3 = 10-9  �L = 10-6 nL = 10-3 pL
1 �m3 = 10-15 L

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