Volume Of Torus Sector Calculator

Volume Of Torus Sector Formula:

\[ V_{Sector} = 2\pi^2 \times r \times r_{Circular\ Section}^2 \times \frac{\angle_{Intersection}}{2\pi} \]

Radius of Torus (r):

Radius of Circular Section of Torus:

Angle of Intersection of Torus Sector:

rad

Volume of Torus Sector:

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1. What is the Volume of Torus Sector?

The Volume of Torus Sector is the amount of three dimensional space occupied by a sector of a torus. A torus is a doughnut-shaped surface generated by rotating a circle in three-dimensional space about an axis coplanar with the circle.

2. How Does the Calculator Work?

The calculator uses the Volume of Torus Sector formula:

\[ V_{Sector} = 2\pi^2 \times r \times r_{Circular\ Section}^2 \times \frac{\angle_{Intersection}}{2\pi} \]

Where:

\( r \) — Radius of Torus (m)
\( r_{Circular\ Section} \) — Radius of Circular Section of Torus (m)
\( \angle_{Intersection} \) — Angle of Intersection of Torus Sector (radians)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula calculates the volume of a torus sector by considering the major radius, minor radius, and the intersection angle of the sector.

3. Importance of Volume Calculation

Details: Calculating the volume of torus sectors is important in various engineering and mathematical applications, particularly in geometry, architecture, and mechanical design where toroidal shapes are used.

4. Using the Calculator

Tips: Enter the radius of torus and radius of circular section in meters, and the angle of intersection in radians. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a torus?
A: A torus is a surface of revolution generated by revolving a circle in three-dimensional space about an axis that is coplanar with the circle.

Q2: What units should I use for the inputs?
A: Use meters for radius measurements and radians for the angle. The result will be in cubic meters.

Q3: Can I use degrees instead of radians?
A: The calculator requires radians. To convert degrees to radians, multiply degrees by π/180.

Q4: What is the range of valid values?
A: All radius values must be positive numbers greater than zero. The angle must be between 0 and 2π radians.

Q5: Where is this calculation used in real life?
A: Torus volume calculations are used in various fields including architecture (designing toroidal structures), engineering (piping systems), and manufacturing (doughnut-shaped objects).