Cap Radius of Spherical Cap given Total Surface Area Calculator

Formula Used:

\[ r_{Cap} = \sqrt{\frac{TSA}{\pi} - (2 \times r_{Sphere} \times h)} \]

Total Surface Area of Spherical Cap (TSA):

m²

Sphere Radius of Spherical Cap (rSphere):

Height of Spherical Cap (h):

Cap Radius of Spherical Cap (rCap):

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1. What is the Cap Radius of Spherical Cap?

The Cap Radius of a Spherical Cap is the radius of the base circle of a Spherical Cap, which is a portion of a sphere cut off by a plane.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_{Cap} = \sqrt{\frac{TSA}{\pi} - (2 \times r_{Sphere} \times h)} \]

Where:

\( r_{Cap} \) — Cap Radius of Spherical Cap (m)
\( TSA \) — Total Surface Area of Spherical Cap (m²)
\( \pi \) — Archimedes' constant (≈3.1416)
\( r_{Sphere} \) — Sphere Radius of Spherical Cap (m)
\( h \) — Height of Spherical Cap (m)

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

3. Importance of Cap Radius Calculation

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

4. Using the Calculator

Tips: Enter total surface area in m², sphere radius in m, and height in m. 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: What are the units for the inputs and outputs?
A: The calculator uses meters (m) for length measurements and square meters (m²) for area measurements.

Q3: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal values with up to 4 decimal places for precise calculations.

Q4: What if I get a negative value under the square root?
A: A negative value under the square root indicates that the input values are not physically possible for a spherical cap. Please verify your inputs.

Q5: How accurate is this calculation?
A: The calculation uses the mathematical constant π with high precision, providing results accurate to 6 decimal places.