Over a century and a half ago, wood was milled a true 2" x 4" ....thus 2x4 .....the same with 2x6, 2x8 ....and so on. However it was "rough sawn" lumber. Wood size standards came about in the 1920 's or so. still made chnges in the mid 60's
But the need for more finished lumber drove sawmills to go through another step in the milling process.. saw mills were crude and milled in crude dimentions. if the mill surfaced one side it was S1S......Surfaced ! Side.... S2S ..and so one.
Economics was the real player in all this ...The new surfaced sizes became the standard...
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Diameter X 3.14159265 divided by 4 X diameter X diameter. 2 * 3.14159265 / 4 * 2 * 2 = 6.2831853 square inches
Approximately 3 1/2 X 3 1/2 inches.
2 x 4 x 6 = 48 2 x 4 x 2 = 16 2 x 6 x 2 = 24 48 + 24 + 16 = 88 square inches
It is: 2 feet times 2 feet = 4 square feet
The VOLUME is 4 x 2 x 6 = 48 inches cubed