The fraction three quarters has a particular interest to biologists because of its link to the research of Max Kleiber and metabolic rates in animals.
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This video features Thomas Woolley from the University of Oxford.
Tom thanks @gameboygenius for pointing out the following: Small mistake. I think where you said they expected MR ∝ r^(2/3) you actually meant to say MR ∝ m^(2/3). If you take the r/V/A relations and solve for A, you get A ∝ V^(2/3). Mass is proportional to volume, so roughly A ∝ m^(2/3). If we then assume MR is proportional to area, the final assumption would be MR ∝ m^(2/3)."
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