Radius Of Circular Section Of Torus Given Radius And Total Surface Area Calculator

Formula Used:

\[ \text{Radius of Circular Section of Torus} = \frac{\text{Total Surface Area of Torus}}{4\pi^2 \times \text{Radius of Torus}} \]

Radius of Circular Section of Torus:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Radius of Circular Section of Torus?

The Radius of Circular Section of Torus is the distance from the center of the circular cross-section to any point on the circumference of that circular cross-section of the Torus. It helps define the size and geometry of the torus shape.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Radius of Circular Section} = \frac{\text{Total Surface Area}}{4\pi^2 \times \text{Radius of Torus}} \]

Where:

\( \pi \) — Archimedes' constant (approximately 3.14159)
Total Surface Area — The complete surface area of the torus (m²)
Radius of Torus — The distance from the center of the torus to the center of the tube (m)

Explanation: This formula derives from the surface area calculation of a torus and allows us to find the cross-sectional radius when we know the total surface area and the main radius.

3. Importance of Circular Section Radius Calculation

Details: Calculating the circular section radius is essential in geometry, engineering, and architectural design where torus shapes are used. It helps in determining the proportions and structural properties of toroidal objects.

4. Using the Calculator

Tips: Enter the total surface area in square meters and the radius of the torus in meters. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a torus?
A: A torus is a doughnut-shaped surface generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.

Q2: How is the total surface area of a torus calculated?
A: The total surface area of a torus is calculated as \( 4\pi^2 \times R \times r \), where R is the radius of the torus and r is the radius of the circular section.

Q3: What are typical applications of torus geometry?
A: Torus geometry is used in various fields including architecture (domes, arches), engineering (pipes, tires), and physics (magnetic confinement in fusion reactors).

Q4: Can this calculator handle different units?
A: The calculator uses meters for length units. If you have measurements in other units, convert them to meters first for accurate results.

Q5: What if I get a negative result?
A: The radius of circular section should always be a positive value. If you get a negative result, check that your input values are positive and valid.