An interesting recent development is a growing awareness of bacteria. It’s now r

Question

An interesting recent development is a growing awareness of bacteria. It’s now realized that the total biomass of bacteria on earth far outweighs all animals, plants, and other complex living beings put together. A recent claim is that “there are 10 times as many bacterial cells in a typical human body as there are human cells.” If we don’t count blood and bone (about 20% of your mass) estimate the fraction of your mass that is bacterial and not “you”. (A set of approximate biological scales is shown below.) Be sure to clearly state your assumptions and how you came to the numbers you estimated, since grading on this problem will be mostly based on your reasoning, not on your answer.

The problem also says that 1 bacterial cell is equal to 1 micrometer while a human cell is equal to 10 micrometers. I think this could be used as a conversion factor.

Explanation / Answer

Let mass of a normal person be 80 kg
then mass to be considered, ignoring blood and bones, m = 0.8*80 = 64 kg

density of humnan body, on an average is rho = 985 kg/m^3
so volume of human body,V = rho/m = 985/64 = 15.39 m^3
if there are n human cells in this volume, then the claim states thet there are 10n bacterial cells
diameter of human cell, d = 10 micro m
diameter of bacterial cell, D = 1 micro m
volume occupied by human cell v = 4*pi*d^3/8
volume occupied by bacterial cell V = 4*pi*D^3/8

so accoringly
nv + 10n*V = 15.39 m^3
4*pi*n(d^3 + 10*D^3)/8 = 15.39
4*pi*n((10*10^-6)^3 + 10*(10^-6)^3)/8 = 15.39
n = 9.7*10^15

hence there are 9.7*10^15 cells of human body in human body
and 9.7*10^16 cells of bacteria

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