Volume Calculation for a Truncated Cone 3B. Oblique Cut Angle = Base Angle °
Author: J007BONDExecutions: 114
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Calculate the volume V of the portion to the right of the cross-section (the shaded area) when a right circular cone with radius R and base angle δ is cut by a plane intersecting the base at an angle γ.Since this function only handles cases where the cutting angle γ exactly matches the base angle δ, the input value for γ should generally be the same as δ.
If γ is smaller than δ, use (3) as described in the “Related Programs” section at the end; if γ is larger than δ, use (5). However, if the value of γ is extremely close to δ (with a difference of 1/100,000,000 or less), calculation errors will occur with those programs, so it is better to use this program.(In such cases, enter the γ value—which differs slightly from δ—into this program as is.)
| Volume V |
[Source of the Formula] Atsuta Shrine Mathematical Inscription
Copy the URL below, click it online to open the site, and you can find it under “Aichi Prefecture, Atsuta Shrine 4.”
Wasan no Yakata: http://www.wasan.jp/
[Paper Proving the Correctness of the Formula] Formula for the Volume of a Truncated Cone and Its Derivation and Proof
Copy the URL below and click it online to view the paper.
https://drive.google.com/file/d/1AuNbqzPdPuiJhn0739EdncBrsuF9Ik-o/view?usp=sharing
[Related Programs] List of the “Volume Calculation for Truncated Cones” Series
If the conditions cannot be calculated using the program above, you can select one of the following options to perform the calculation.
(1) Volume Calculation for Truncated Cones 1. Vertical Truncation°
(2) Volume Calculation for a Truncated Cone 2. Oblique Cut Where the Cut Surface Touches the Base°
(3) Volume Calculation for a Truncated Cone 3A. Oblique Cut Angle Smaller Than the Base Angle°
(4) Volume Calculation for a Truncated Cone 3B. Slant Cut Angle = Base Angle °
(5) Volume Calculation for a Truncated Cone 3C. Slant Cut Angle Greater Than the Base Angle °
Copy the URL below, click it online to open the site, and you can find it under “Aichi Prefecture, Atsuta Shrine 4.”
Wasan no Yakata: http://www.wasan.jp/
[Paper Proving the Correctness of the Formula] Formula for the Volume of a Truncated Cone and Its Derivation and Proof
Copy the URL below and click it online to view the paper.
https://drive.google.com/file/d/1AuNbqzPdPuiJhn0739EdncBrsuF9Ik-o/view?usp=sharing
[Related Programs] List of the “Volume Calculation for Truncated Cones” Series
If the conditions cannot be calculated using the program above, you can select one of the following options to perform the calculation.
(1) Volume Calculation for Truncated Cones 1. Vertical Truncation°
(2) Volume Calculation for a Truncated Cone 2. Oblique Cut Where the Cut Surface Touches the Base°
(3) Volume Calculation for a Truncated Cone 3A. Oblique Cut Angle Smaller Than the Base Angle°
(4) Volume Calculation for a Truncated Cone 3B. Slant Cut Angle = Base Angle °
(5) Volume Calculation for a Truncated Cone 3C. Slant Cut Angle Greater Than the Base Angle °
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