1. What is a Torus (Donut Shape)?

A torus is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle. It's the mathematical term for what we commonly call a donut shape.

2. How Does the Calculator Work?

The calculator uses the torus surface area formula:

Where:

• \( R \) — 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 surface area by considering the product of the two radii and the fundamental geometric constant π.

3. Importance of Torus Calculations

Details: Understanding torus geometry is important in various fields including physics (magnetic confinement in tokamaks), engineering (design of tires and pipes), and architecture (unique structural designs).

4. Using the Calculator

Tips: Enter both radii in the same units (e.g., centimeters or inches). Both 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 tube to the center of the torus, while the minor radius (r) is the radius of the tube itself.

Q2: Can I use this for a partial torus?
A: No, this formula calculates the complete surface area of a full torus. Partial torus calculations require more complex formulas.

Q3: What if my torus isn't perfectly circular?
A: This formula assumes perfect circular symmetry. For non-circular tori, numerical methods may be needed.

Q4: How is this related to volume calculations?
A: The volume of a torus is given by \( V = 2\pi^2 R r^2 \), which is different from the surface area formula.

Q5: What are some real-world applications?
A: Torus shapes are used in tire design, nuclear fusion reactors (tokamaks), lifebuoys, and many architectural structures.