Lateral Surface Area Of Torus Sector Given Volume And Major Radius Calculator

Formula Used:

\[ LSASector = \left(4 \times \pi^2 \times \frac{VSector}{2 \times \pi^2 \times rCircularSection^2 \times \frac{\angle Intersection}{2\pi}}\right) \times rCircularSection \times \frac{\angle Intersection}{2\pi} \]

Volume of Torus Sector (VSector):

m³

Radius of Circular Section of Torus (rCircularSection):

Angle of Intersection of Torus Sector (∠Intersection):

rad

Lateral Surface Area of Torus Sector (LSASector):

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1. What is Lateral Surface Area of Torus Sector?

The Lateral Surface Area of Torus Sector is the total quantity of two-dimensional plane enclosed on the lateral curved surface of the Torus Sector. It represents the surface area excluding the top and bottom circular faces of the sector.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

\( LSASector \) — Lateral Surface Area of Torus Sector (m²)
\( VSector \) — Volume of Torus Sector (m³)
\( rCircularSection \) — 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 lateral surface area based on the volume and geometric properties of the torus sector.

3. Importance of Lateral Surface Area Calculation

Details: Calculating lateral surface area is important in various engineering and architectural applications where torus-shaped structures are used, particularly in determining material requirements and surface coverage.

4. Using the Calculator

Tips: Enter volume in cubic meters (m³), radius in meters (m), and angle in radians (rad). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a torus sector?
A: A torus sector is a portion of a torus (doughnut-shaped object) bounded by two planes that intersect the torus.

Q2: How is this different from total surface area?
A: Lateral surface area excludes the circular end faces of the sector, while total surface area includes all surfaces.

Q3: What units should I use for the inputs?
A: Use consistent units (preferably SI units: meters for length, cubic meters for volume, and radians for angle).

Q4: Can this formula be used for any torus sector?
A: Yes, this formula is applicable for any torus sector with the given parameters.

Q5: What if I have the angle in degrees instead of radians?
A: Convert degrees to radians by multiplying by π/180 before entering the value.