1. What is a Torus (Donut)?

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. In simpler terms, it's the mathematical name for a donut shape.

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)
• \( \pi \) — Mathematical constant (~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 Volume Calculation

Details: Calculating the volume of a torus is important in various fields including engineering, architecture, and manufacturing where donut-shaped objects are used.

4. Using the Calculator

Tips: Enter both radii in centimeters. The major radius (R) should be larger than the minor radius (r). Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

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

Q2: Can I use this for partial torus shapes?
A: No, this formula is for complete, circular toruses. Partial toruses require more complex calculations.

Q3: What if my donut isn't perfectly circular?
A: This formula assumes perfect circular symmetry. For non-circular shapes, other methods like numerical integration would be needed.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact for perfect torus shapes with the given dimensions.

Q5: Can I use different units?
A: The calculator uses centimeters, but you can use any unit as long as you're consistent - the result will be in cubic units of whatever you input.