Radius of Spherical Segment Calculator

Formula Used:

\[ r = \sqrt{r_{Base}^2 + \left( \frac{r_{Base}^2 - r_{Top}^2 - h^2}{2h} \right)^2} \]

Base Radius of Spherical Segment:

Top Radius of Spherical Segment:

Height of Spherical Segment:

Radius of Spherical Segment:

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1. What is the Radius of Spherical Segment?

The Radius of Spherical Segment is the line segment extending from the center to the circumference of the sphere in which the Spherical Segment is bounded. It represents the radius of the complete sphere from which the segment is derived.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r = \sqrt{r_{Base}^2 + \left( \frac{r_{Base}^2 - r_{Top}^2 - h^2}{2h} \right)^2} \]

Where:

\( r \) — Radius of Spherical Segment (m)
\( r_{Base} \) — Base Radius of Spherical Segment (m)
\( r_{Top} \) — Top Radius of Spherical Segment (m)
\( h \) — Height of Spherical Segment (m)

Explanation: This formula calculates the radius of the complete sphere based on the dimensions of the spherical segment, using geometric relationships between the base radius, top radius, and height.

3. Importance of Radius Calculation

Details: Calculating the radius of the complete sphere from a spherical segment is important in various geometric and engineering applications, including architectural design, manufacturing, and spatial analysis where spherical segments are used.

4. Using the Calculator

Tips: Enter the base radius, top radius, and height of the spherical segment in meters. All values must be positive numbers, with base radius and height greater than zero.

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 top radius be zero?
A: Yes, when the top plane passes through the center of the sphere, the top radius becomes zero, creating a spherical cap.

Q3: What units should I use?
A: The calculator uses meters, but you can use any consistent unit of length as long as all inputs are in the same unit.

Q4: Are there limitations to this formula?
A: The formula assumes a perfect spherical segment and may not be accurate for irregular shapes or when the segment dimensions don't correspond to a valid sphere.

Q5: How is this different from spherical cap calculations?
A: A spherical cap is a special case of a spherical segment where one of the bases has zero radius (rTop = 0).