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Diameter vs. mass Sun, Mar 23, 2014
I was collecting firewood yesterday, and naturally I was thinking about math.  Specifically, how much more does a log with a larger diameter weigh than a log with a smaller diameter?  Assuming a log is a perfect cylinder, its mass = density*volume = density*(pi/4)*diameter2*length.  For two logs that have the same density and the same length, the change in area is the following: 
Δm = (ρ*(π/4)*d22*ℓ - ρ*(π/4)*d12*ℓ)/(ρ*(π/4)*d12*ℓ) = (d22/d12) - 1
It's actually the same result as pizza math.  What this means in reality is that a log that's 15 inches in diameter compared to a log that's 7 inches in diameter (114% increase, or 2.1 times) is (152/72)-1 = 359% (4.6 times) heavier.  More generally, a log with x times the diameter will weigh x2 times as much.  And that's why my back hurts today. #math

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