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 seen in objects like inner tubes, rings, and some types of piping.

2. How Does the Calculator Work?

The calculator uses the torus volume formula:

Where:

• \( R \) — Major radius (distance from center of tube to center of torus)
• \( r \) — Minor radius (radius of the tube)
• \( V \) — Volume of the torus

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 engineering, architecture, and manufacturing where toroidal shapes are used, such as in pressure vessels, piping systems, and certain structural components.

4. Using the Calculator

Tips: Enter both radii in consistent units (e.g., meters, inches). The major radius must be larger than the minor radius for a standard torus. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between major and minor radius?
A: The major radius (R) is the distance from the center of the torus to the center of the tube, while the minor radius (r) is the radius of the circular 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 for horn (R = r) and spindle (R < r) tori.

Q3: What are real-world applications of torus volume calculations?
A: Applications include calculating material needed for toroidal containers, determining capacity of donut-shaped tanks, and designing toroidal components in machinery.

Q4: How does the volume change if I double the major radius?
A: The volume is directly proportional to the major radius, so doubling R will double the volume (assuming r stays constant).

Q5: What if I double the minor radius instead?
A: Since volume depends on r², doubling the minor radius will quadruple the volume (assuming R stays constant).