Total Surface Area Of Torus Sector Given Lateral Surface Area And Radius Calculator

Formula Used:

\[ TSASector = (LSASector + (2 \times \pi \times \left( \frac{LSASector}{4 \times \pi^2 \times r \times \frac{\angle Intersection}{2\pi}} \right)^2)) \]

Lateral Surface Area of Torus Sector (LSASector):

m²

Radius of Torus (r):

Angle of Intersection (∠Intersection):

rad

Total Surface Area of Torus Sector (TSASector):

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1. What is Total Surface Area of Torus Sector?

The Total Surface Area of Torus Sector is the total quantity of two dimensional space enclosed on the entire surface of the Torus Sector, including both lateral and base areas.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSASector = (LSASector + (2 \times \pi \times \left( \frac{LSASector}{4 \times \pi^2 \times r \times \frac{\angle Intersection}{2\pi}} \right)^2)) \]

Where:

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

Explanation: This formula calculates the total surface area by adding the lateral surface area to the area of the two circular end faces of the torus sector.

3. Importance of Torus Sector Calculation

Details: Calculating the total surface area of torus sectors is important in various engineering and architectural applications, particularly in the design of curved structures and mechanical components with toroidal shapes.

4. Using the Calculator

Tips: Enter lateral surface area in square meters, radius in meters, and angle in radians. 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 bounded by two planes that intersect the torus, creating a curved 3D shape with circular cross-sections.

Q2: Why is the angle measured in radians?
A: Radians are used because they provide a natural measurement of angle in mathematical calculations involving circles and circular motion.

Q3: Can this calculator handle different units?
A: The calculator uses consistent SI units (meters for length, square meters for area, radians for angles). Convert your measurements to these units before calculation.

Q4: What are typical applications of torus sector calculations?
A: Applications include architectural design of curved structures, mechanical engineering of toroidal components, and mathematical modeling of curved surfaces.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the provided formula, assuming precise input values and proper unit conversion.