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Would You Please Repeat that Slowly....

To gauge a cask, that is, to find how much it holds, Find on the inside in inches, the length, the bung diameter, and the head diameter; then if the staves be much curved between the bung and head, add to the head diameter 2/3 of the difference between the bung and head diameters; but if the staves be but little curved, add 3/5 of the difference; the sum is found by experience, to be about the diameter of a cylinder of the same length and capacity as the cask; the quantity contained in the cylinder is the quantity the cask will hold.




Solution:

Source: George Leonard's A Practical treatise on Arithmetic, 1841, p. 221