Radius Of Torus Given Lateral Surface Area Of Torus Sector Calculator

Formula Used:

\[ r = \frac{LSASector}{4 \times \pi^2 \times rCircular Section \times \frac{\angle Intersection}{2\pi}} \]

Lateral Surface Area of Torus Sector (LSASector):

m²

Radius of Circular Section of Torus (rCircular Section):

Angle of Intersection of Torus Sector (∠Intersection):

rad

Radius of Torus (r):

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1. What is the Radius of Torus?

The Radius of Torus is the line connecting the center of the overall Torus to the center of a circular cross-section of the Torus. It is a fundamental parameter in torus geometry that determines the overall size and shape of the torus.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r = \frac{LSASector}{4 \times \pi^2 \times rCircular Section \times \frac{\angle Intersection}{2\pi}} \]

Where:

\( r \) — Radius of Torus (m)
\( LSASector \) — Lateral Surface Area of Torus Sector (m²)
\( rCircular Section \) — Radius of Circular Section of Torus (m)
\( \angle Intersection \) — Angle of Intersection of Torus Sector (rad)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: This formula calculates the radius of a torus based on the lateral surface area of a torus sector, the radius of its circular cross-section, and the intersection angle.

3. Importance of Radius Calculation

Details: Calculating the radius of a torus is essential in various engineering and mathematical applications, including mechanical design, architectural structures, and geometric modeling. It helps determine the overall dimensions and properties of toroidal objects.

4. Using the Calculator

Tips: Enter the lateral surface area of the torus sector in square meters, the radius of the circular section in meters, and the angle of intersection in radians. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a torus?
A: A torus is a three-dimensional geometric shape that resembles a doughnut or inner tube, formed by revolving a circle in three-dimensional space about an axis coplanar with the circle.

Q2: What is 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 tube itself.

Q3: Can this calculator handle different units?
A: The calculator uses meters for length units and radians for angles. Convert your measurements to these units before calculation for accurate results.

Q4: What if my angle is in degrees?
A: Convert degrees to radians by multiplying by π/180 (approximately 0.0174533) before entering the value.

Q5: Are there any limitations to this formula?
A: This formula is specifically designed for calculating the radius of a torus given the lateral surface area of a torus sector and assumes standard geometric properties of a perfect torus.