#1 Cut cone volume, vertically (cutting angle γ=90 deg.)    Execution: 110

When a straight cone with radius R and base angle δ is cut vertically (parallel to the central axis), the volume V of the cut part (shaded part) on the right side of the cut surface is obtained.

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

volume V
    1.  
#1  Cut cone volume, 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 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.)
https://drive.google.com/file/d/1AuNbqzPdPuiJhn0739EdncBrsuF9Ik-o/view?usp=sharing

【Reference】 Cut cone volume calculation programs
In case the above program is not applicable, select the proper one from the series of “Cut cone volume” programs listed below:
(1) #1 Cut cone volume, vertically (cutting angle γ=90 deg.)
(2) #2 Cut cone volume, slantly, by plane tangent to base circle
(3) #3A Cut cone volume, slantly, cutting angle γ<base angle δ
(4) #3B Cut cone volume, slantly, cutting angle γ=base angle δ
(5) #3C Cut cone volume, slantly, cutting angle γ>base angle δ


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