1. What is a Torus?

A torus is a doughnut-shaped surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle. It's commonly found in mathematics, physics, and engineering applications.

2. How Does the Calculator Work?

The calculator uses the torus volume formula:

Where:

• \( V \) — Volume of the torus (cubic units)
• \( R \) — Major radius (distance from center of tube to center of torus)
• \( r \) — Minor radius (radius of the tube)
• \( \pi \) — Mathematical constant pi (~3.14159)

Explanation: The formula calculates the volume by multiplying the area of the circular cross-section (πr²) by the circumference of the path traced by its center (2πR).

3. Importance of Torus Volume Calculation

Details: Calculating torus volume is important in various fields including architecture (designing circular structures), physics (modeling magnetic fields in tokamaks), and manufacturing (designing pipes and rings).

4. Using the Calculator

Tips: Enter both radii in consistent units (both in meters, inches, etc.). The major radius must be larger than the minor radius for a standard torus.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between R and r?
A: R is the distance from the center of the torus to the center of the tube, while r is the radius of the tube itself.

Q2: Can this formula be used for a horn torus or spindle torus?
A: No, this formula is specifically for a ring torus where R > r. Different formulas apply when R = r (horn torus) or R < r (spindle torus).

Q3: What are real-world examples of torus shapes?
A: Common examples include doughnuts, inner tubes, lifebuoys, and some types of piping.

Q4: How is this different from a cylinder's volume?
A: A cylinder's volume is πr²h (height × base area), while a torus volume accounts for the circular path of the rotated cylinder.

Q5: What if I only know the diameter measurements?
A: Simply divide the diameters by 2 to get the radii before entering them into the calculator.