Volume Calculation for a Truncated Cone, 3A. The angle of the oblique cut is less than the base angle by °
Author: J007BONDExecutions: 189
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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.
The formula provided here applies only when the cut angle γ is smaller than the base angle δ. Since the formula differs under other conditions, it is provided separately in a different program.
[Note] 1. If the cut angle γ is negative, the calculated volume V will be negative; therefore, use the absolute value. 2. When γ = 0, the calculation will result in an error, but it is self-evident that the volume V is 0 in that case.
[Note] 1. If the cut angle γ is negative, the calculated volume V will be negative; therefore, use the absolute value. 2. When γ = 0, the calculation will result in an error, but it is self-evident that the volume V is 0 in that case.
| Volume V |
[Source of the Formula] Atsuta Jingu Shrine Mathematical Inscription
Copy the URL below, click it online to open the site, and you can find it under “Aichi Prefecture, Atsuta Jingu 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 Jingu 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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