Partial cone volume, #1 vertically (cutting angle γ=90 deg.)    Execution: 51

Calculates the volume of a partial circular cone cut out vertically (parallel to the axis), given the radius of the base circle R, base angle δ and the position where to cut the cone in terms of angle Θ.

Partial cone volume, #1 vertically (cutting angle γ=90 deg.)
Base circle radius R
    1. °
Base angle δ
    1. °
Cut position (angle) Θ
    1. °

Volume V
    1.  
Partial cone volume, #1 vertically (cutting angle γ=90 deg.)
【Source of formula】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 formula by Index "Aichi pref. Atsuta Jingu 4".

【Thesis on derivation of formula for proof of correctness】
  Copy and paste the following URL and click it on the Net to find the thesis on derivation of the formula. (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.)
https://drive.google.com/file/d/1AuNbqzPdPuiJhn0739EdncBrsuF9Ik-o/view?usp=sharing

【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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