Partial cone volume, #3A diagonal, cutting angle＜base angle Execution: 20
Calculates the volume of a partial circular cone cut out diagonally by a plane crossing the base circle, given the radius of the base circle R, base angle δ, where it is cut in terms of angle Θ and the cutting angle γ which is smaller than the base angle δ.
|【Source of formulae】Atsuta Jingu Sangaku|
Search for the "Wasan no yakata" site by URL http://www.wasan.jp/, and one can find a sangaku picture showing the above formulae by Index "Aichi pref. Atsuta Jingu 4".
【Thesis on derivation of formulae for proof of correctness】
Copy and paste the following URL and click it on the Net to find the thesis on derivation of the formulae. (The thesis is written in Japanese, but anyone can easily understand it without knowing the Japanese language because the main part is written in ordinary mathematical expression.)
【Reference】 Partial cone volume calculation programs
In case the above program is not applicable, select the proper one from the series of “Partial cone volume” programs listed below:
(1) Partial cone volume, #1 vertically (cutting angle γ=90 deg.)
(2) Partial cone volume, #2 diagonal, cut at edge of base circle
(3) Partial cone volume, #3A diagonal, cutting angle＜base angle
(4) Partial cone volume, #3B diagonal, cutting angle＝base angle
(5) Partial cone volume, #3C diagonal, cutting angle＞base angle
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Partial cone volume, #3A diagonal, cutting angle＜base angle
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