Radius of Spherical Segment given Total Surface Area Calculator

Formula Used:

\[ r = \frac{TSA - \pi \cdot (r_{Base}^2 + r_{Top}^2)}{2 \pi h} \]

Total Surface Area of Spherical Segment (TSA):

m²

Base Radius of Spherical Segment (rBase):

Top Radius of Spherical Segment (rTop):

Height of Spherical Segment (h):

Radius of Spherical Segment (r):

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1. What is the Radius of Spherical Segment?

The radius of a spherical segment is the distance from the center of the sphere to the surface of the spherical segment. It is a fundamental parameter in spherical geometry that helps define the size and shape of the segment.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r = \frac{TSA - \pi \cdot (r_{Base}^2 + r_{Top}^2)}{2 \pi h} \]

Where:

\( r \) — Radius of Spherical Segment (m)
\( TSA \) — Total Surface Area of Spherical Segment (m²)
\( r_{Base} \) — Base Radius of Spherical Segment (m)
\( r_{Top} \) — Top Radius of Spherical Segment (m)
\( h \) — Height of Spherical Segment (m)
\( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: The formula calculates the radius of the sphere from which the spherical segment is derived, using the total surface area and other dimensional parameters.

3. Importance of Radius Calculation

Details: Calculating the radius of a spherical segment is essential in various engineering and architectural applications, particularly in designing domed structures, tanks, and other spherical components where precise measurements are critical.

4. Using the Calculator

Tips: Enter all values in meters. Ensure that the total surface area is greater than the sum of the areas of the top and bottom bases for valid results. All input values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a spherical segment?
A: A spherical segment is the solid portion of a sphere cut off by two parallel planes. It has two circular bases and a curved surface.

Q2: Can the radius be negative?
A: No, the radius is always a positive value as it represents a physical distance from the center to the surface.

Q3: What if the denominator becomes zero?
A: If the height is zero, the denominator becomes zero and the radius is undefined, as a spherical segment cannot have zero height.

Q4: Are there any limitations to this formula?
A: This formula assumes perfect spherical geometry and may not account for real-world imperfections or deformations in spherical structures.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise for ideal spherical segments. Accuracy in practical applications depends on the precision of input measurements.