tonybenwhite

tonybenwhite t1_irv2wr8 wrote

Did some noodling:

Pencil graphite lays a 20micron thick layer. Colored pencil leaves a bit thicker, and since I couldn’t find any source that talks about how thick that is, I’ll approximate twice as thick as graphite.

At 40 microns, that creates 1,577.5 discs by evenly segmenting the 63.1mm height of the cylinder of the used core of the black pencil.

Finding the sum of the areas of 1,577.5 circles with a 10mm diameter should give us surface coverage with the formula:

π r² • 1,577.5 circles

= π 5mm² • 1,577.5 circles

= 123,896.6mm²

or 1,239.0cm² or 0.1m² or 1.3ft² for my Yankees out there

With an additional assumption the pencil stayed sharp without any loss to a sharpening process, for which I’m too lazy to calculate what a reasonable margin of error might be for loss in shavings.

Another assumption of consistent pressure. There’s certainly a coefficient of pressure that affects the pencil lead thickness, e.g. increasing the number of cylinder segments with lighter drawing

Tbh though this seems low to me. So maybe my noodling flopped

The rest would be as follows if my math didn’t completely suck:

  • Black: 0.1239m^2 or 1.3336ft^2
  • Red: 0.1005m^2 or 1.0821ft^2
  • Violet: 0.0719m^2 or 0.7735ft^2
  • Blue: 0.0785m^2 or 0.8454ft^2
  • White: 0.0827m^2 or 0.8898ft^2
  • Yellow: 0.0827m^2 or 0.8898ft^2
  • Orange: 0.0807m^2 or 0.8686ft^2
  • Green: 0.0685m^2 or 0.7376ft^2
  • Pink: 0.0685m^2 or 0.7376ft^2
  • Teal: 0.0620m^2 or 0.6679ft^2
  • Tan: 0.0511m^2 or 0.5495ft^2
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