1. What is the Sphere Radius of Spherical Cap?

The Sphere Radius of Spherical Cap is the radius of the sphere from which the Spherical Cap shape is cut. It represents the original sphere's size before the cap was removed.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: This formula calculates the original sphere's radius using the total surface area and height of the spherical cap.

3. Importance of Sphere Radius Calculation

Details: Calculating the sphere radius is essential in geometry and engineering applications where spherical caps are used, such as in dome construction, tank design, and various architectural elements.

4. Using the Calculator

Tips: Enter the total surface area in square meters and the height in meters. Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a spherical cap?
A: A spherical cap is a portion of a sphere cut off by a plane. It consists of a circular base and a curved surface.

Q2: How is this different from the cap radius?
A: The sphere radius refers to the original sphere's size, while the cap radius refers to the radius of the circular base of the cap.

Q3: What are typical applications of this calculation?
A: This calculation is used in architectural design, manufacturing of spherical containers, and various engineering applications involving spherical surfaces.

Q4: Are there limitations to this formula?
A: The formula assumes a perfect spherical shape and may not be accurate for irregular or deformed spheres.

Q5: Can this be used for partial spheres?
A: Yes, this formula specifically calculates the original sphere radius from which a spherical cap has been cut.