#2 Cut cone volume, slantly by plane tangent to base circle    Execution: 51

When a straight cone with radius R and base angle δ is cut diagonally by a plane tangent to the bottom circle at an angle γ, the volume V of the cut part (shaded part) on the right side of the cut surface and that of the left part Vu after cutting are obtained.

#2  Cut cone volume, slantly by plane tangent to base circle
Base angle δ
    1. °
Cutting angle γ
    1. °
Base circle radius R

Volume V
    1.  
Volume Vu
    1.  
#2  Cut cone volume, slantly by plane tangent to base circle
【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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