Sphere Radius of Spherical Cap Given Total Surface Area and Cap Radius Calculator

Formula Used:

\[ r_{Sphere} = \frac{TSA - \pi \cdot r_{Cap}^2}{2 \pi \cdot h} \]

Total Surface Area of Spherical Cap (TSA):

m²

Cap Radius of Spherical Cap (rCap):

Height of Spherical Cap (h):

Sphere Radius of Spherical Cap (rSphere):

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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 section was removed.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_{Sphere} = \frac{TSA - \pi \cdot r_{Cap}^2}{2 \pi \cdot h} \]

Where:

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

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

3. Importance of Sphere Radius Calculation

Details: Calculating the sphere radius is crucial 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 total surface area in square meters, cap radius in meters, and height in meters. All values must be positive numbers.

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: When is this calculation useful?
A: This calculation is useful in architecture, engineering, and manufacturing where spherical shapes are involved, particularly when working with partial spheres or domes.

Q3: What are the units for measurement?
A: The calculator uses meters for length measurements and square meters for area measurements. Ensure consistent units for accurate results.

Q4: Are there limitations to this formula?
A: The formula assumes perfect spherical geometry and may not account for real-world imperfections or variations in material thickness.

Q5: Can this be used for hemispheres?
A: Yes, a hemisphere is a special case of a spherical cap where the height equals the sphere radius.