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October 9

Trying to resolve a discrepancy

I am trying to resolve an (apparent) discrepancy. Any help is appreciated. Thanks in advance.

Here is a website: [1].

About half-way down that page, there is a (somewhat) complicated formula:

Volume (L,R,h) = L[R^2cos^(-1)((R-h)/R)-(R-h)sqrt(2Rh-h^2)]

In that formula, we can replace the variable "L" (Length) with the known value of 192.

In that formula, we can also replace the variable "R" (Radius) with the known value of 48.

Now, we move on to a completely different website: [2].

In this second website, someone has converted the above mathematical formula into an Excel formula.

The variable "h" (Height) is replaced with the Excel Cell Number labeled K2.

Towards the very bottom of the page, on the second website, the proposed "Excel" translation formula for the above mathematical formula is given as:

Volume = 192*(48^2*ACOS((48-K2)/48)-(48-K2)*PIERWIASTEK(2*48*K2-K2^2))/231.

That person states to replace the gibberish phrase of "PIERWIASTEK" with whatever the correct Excel formula is for Square Root (which is "SQRT").

In summary:

Original mathematical formula: Volume = L[R^2cos^(-1)((R-h)/R)-(R-h)sqrt(2Rh-h^2)]

Proposed "Excel" translation: Volume = 192*(48^2*ACOS((48-K2)/48)-(48-K2)*SQRT(2*48*K2-K2^2))/231.

To me, everything seems to "line up" pretty much perfectly.

I just can't seem to figure out why the Excel formula has that "extra" calculation added in at the very end ... namely, to divide by 231.

As all of the elements between both formulas seem (to me) to line up and match, pretty exactly ... why is the person throwing in that extra "divide by 231" at the end?

Thanks! 32.209.55.38 (talk) 05:30, 9 October 2022 (UTC)[reply]

The number 231 is a conversion factor because the answer is supposed to be in gallons, and 1 US gallon is 231 cubic inches. The word pierwiastek is Polish for "root". The term for square root is more fully pierwiastek kwadratowy, but just pierwiastek is a common shortening. --Lambiam 17:10, 9 October 2022 (UTC)[reply]

@Lambian: Thank you so much! Just want to clarify, to make sure I understand. Both formulas are correct. The first one (the mathematical formula) simply gives the result in cubic inches ... while the second one (the Excel translation) gives the result in gallons. Other than that, the two formulas are exactly the same. Right? Thank you so much! 32.209.55.38 (talk) 21:18, 11 October 2022 (UTC)[reply]

That is correct. More precisely, the first formula gives the result in the same units as used for the values of L, R and h, whatever they are, raised to the third. Inches in, cubic inches out, Furlongs in, cubic furlongs out. Assuming that the numeric quantities 192 and 48, as well as the value of K2, are given in inches, the second formula is an application of the first formula, except for a final conversion from cubic inches to gallons. --Lambiam 06:28, 12 October 2022 (UTC)[reply]

I agree with Lambiam, both in the analysis of formulas and in the deciphering of 'pierwiastek'. :) CiaPan (talk) 11:19, 12 October 2022 (UTC)[reply]