Spherical Radius of Spherical Sector given Total Surface Area Calculator

Formula Used:

\[ r_{Sphere} = \frac{TSA}{\pi \times ((2 \times h_{Cap}) + r_{Cap})} \]

Total Surface Area of Spherical Sector:

m²

Spherical Cap Height of Spherical Sector:

Spherical Cap Radius of Spherical Sector:

Spherical Radius of Spherical Sector:

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1. What is Spherical Radius of Spherical Sector?

The Spherical Radius of Spherical Sector is the distance from the center to any point on the surface of the sphere from which the Spherical Sector is cut. It is a fundamental parameter in spherical geometry and 3D spatial calculations.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_{Sphere} = \frac{TSA}{\pi \times ((2 \times h_{Cap}) + r_{Cap})} \]

Where:

\( r_{Sphere} \) — Spherical Radius of Spherical Sector (m)
\( TSA \) — Total Surface Area of Spherical Sector (m²)
\( h_{Cap} \) — Spherical Cap Height of Spherical Sector (m)
\( r_{Cap} \) — Spherical Cap Radius of Spherical Sector (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: This formula calculates the spherical radius based on the total surface area and the dimensions of the spherical cap that forms the sector.

3. Importance of Spherical Radius Calculation

Details: Accurate calculation of spherical radius is crucial for various applications in geometry, physics, engineering, and computer graphics where spherical sectors are involved in 3D modeling and spatial analysis.

4. Using the Calculator

Tips: Enter total surface area in square meters, spherical cap height in meters, and spherical cap radius in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a spherical sector?
A: A spherical sector is a portion of a sphere defined by a conical boundary with apex at the sphere's center and the spherical cap surface.

Q2: How is this different from regular sphere radius?
A: This specifically calculates the radius of the original sphere from which a spherical sector with given parameters was cut.

Q3: What are typical applications of this calculation?
A: Used in architectural design, mechanical engineering, astronomy, and any field dealing with spherical geometry and 3D spatial relationships.

Q4: Are there limitations to this formula?
A: The formula assumes perfect spherical geometry and may not account for irregularities or deformations in real-world objects.

Q5: Can this be used for partial spherical sectors?
A: Yes, the formula works for any spherical sector as long as the total surface area and cap dimensions are accurately measured.