Radius of Outer Circle of Annulus given Longest Interval and Perimeter Calculator

Formula Used:

\[ r_{Outer} = \frac{\left(\frac{P}{2\pi}\right) + \left(\frac{\frac{l^2}{4}}{\left(\frac{P}{2\pi}\right)}\right)}{2} \]

Outer Circle Radius (r_Outer):

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1. What is the Outer Circle Radius of Annulus?

The Outer Circle Radius of Annulus is the radius of the larger circle in a pair of concentric circles that form an annulus. It represents the distance from the center to the outer boundary of the annular region.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_{Outer} = \frac{\left(\frac{P}{2\pi}\right) + \left(\frac{\frac{l^2}{4}}{\left(\frac{P}{2\pi}\right)}\right)}{2} \]

Where:

\( r_{Outer} \) — Outer Circle Radius of Annulus (m)
\( P \) — Perimeter of Annulus (m)
\( l \) — Longest Interval of Annulus (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: This formula calculates the outer radius based on the perimeter and the longest chord (interval) that can be drawn within the annulus, tangent to the inner circle.

3. Importance of Outer Circle Radius Calculation

Details: Calculating the outer radius is essential in various engineering and geometric applications, particularly in designing circular structures, mechanical parts, and understanding annular areas in mathematics and physics.

4. Using the Calculator

Tips: Enter the perimeter and longest interval values in meters. Both values must be positive numbers. The calculator will compute the outer radius using the derived formula.

5. Frequently Asked Questions (FAQ)

Q1: What is an annulus?
A: An annulus is a ring-shaped object, the region bounded by two concentric circles of different radii.

Q2: How is the longest interval of annulus defined?
A: The longest interval is the longest chord that can be drawn within the annulus, which is tangent to the inner circle.

Q3: Can this formula be used for any annulus?
A: Yes, this formula is derived from geometric properties and applies to all annular shapes with concentric circles.

Q4: What are practical applications of this calculation?
A: This calculation is used in mechanical engineering (e.g., pipe design), architecture, and various fields requiring precise circular measurements.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise when correct values are provided, though real-world measurements may have slight variations.