1. What is the Volume of Torus Formula?

The volume of a torus (doughnut shape) is calculated using the formula that relates the overall radius and the hole radius of the torus. This formula provides an accurate measurement of the three-dimensional space occupied by the torus shape.

2. How Does the Calculator Work?

The calculator uses the torus volume formula:

Where:

• \( V \) — Volume of Torus (m³)
• \( \pi \) — Mathematical constant pi (approximately 3.14159)
• \( r \) — Radius of Torus (m)
• \( r_{Hole} \) — Hole Radius of Torus (m)

Explanation: The formula calculates the volume by considering the circular cross-section of the torus and its revolution around the central axis.

3. Importance of Torus Volume Calculation

Details: Calculating torus volume is essential in various engineering applications, architectural designs, and mathematical modeling where torus-shaped objects are involved.

4. Using the Calculator

Tips: Enter the radius of torus and hole radius in meters. Both values must be positive, and the radius must be greater than the hole radius for a valid torus shape.

5. Frequently Asked Questions (FAQ)

Q1: What is a torus?
A: A torus is a three-dimensional shape resembling a doughnut or inner tube, formed by revolving a circle in three-dimensional space about an axis.

Q2: What are the units for torus volume?
A: The volume is typically measured in cubic meters (m³) or other cubic units depending on the input measurements.

Q3: Can the hole radius be zero?
A: If the hole radius is zero, the torus becomes a sphere, but this formula is specifically for torus shapes where radius > hole radius.

Q4: What are practical applications of torus volume calculation?
A: Torus volume calculations are used in engineering (pipe bends, tires), architecture (domed structures), and manufacturing (O-rings, donut-shaped products).

Q5: How accurate is this formula?
A: The formula is mathematically exact for perfect torus shapes and provides precise volume calculations when correct measurements are provided.