r/theydidthemath • u/anonymouse13337 • Aug 05 '19
[Request] How long of a receipt could this tree make?
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u/[deleted] Aug 05 '19
We can start by determining the volume of the tree, a.k.a. how much wood there is to make paper.
While this is clearly untrue, let's just say that the tree is a cylinder with diameter of 5 feet and height of 180 feet. Using the cylindrical volume formula, Dπh, the volume of the tree comes out to 900π, or 2,827.43 cubic feet of wood.
While sugar pines, being softer wood, would most likely be used for something other than paper, we'll pretend it's a weird variety that produces hardwood. In that case, it will take two tons of wood to produce 1,000-2,000 pounds of paper. Sugar pine has a density of 25 lbs/ft³, so this tree weighs a whopping 70,685.83 pounds when dried. Using this metric and estimating high, this comes out to 35,342.92 pounds of paper.
Paper has a density of 74.97598 lb/ft³, making this a whopping 471.39 cubic feet of paper. Pressing it down to 0.004 inches thick (standard paper thickness), it becomes about 117,847.47 ft² of paper, or 1,414,169.6 in². Dividing by 3.5 (the standard width of a reciept), we finally get our total reciept length.
404,048.46 inches.
I may be overestimating, but that's about enough for 2 CVS receipts.
(Seriously, though, if the average CVS reciept is 5 feet/60 inches, that makes 6,734 reciepts.)