Longest Interval of Annulus given Perimeter and Outer Circle Radius Calculator

Formula Used:

\[ l = 2 \times \sqrt{\frac{P}{2\pi} \times \left(2r_{\text{Outer}} - \frac{P}{2\pi}\right)} \]

Longest Interval of Annulus (l):

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1. What is the Longest Interval of Annulus?

The Longest Interval of Annulus is the length of the longest line segment within the Annulus, which is the chord tangent to the inner circle. It represents the maximum distance between two points on the outer circle that doesn't intersect the inner circle.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l = 2 \times \sqrt{\frac{P}{2\pi} \times \left(2r_{\text{Outer}} - \frac{P}{2\pi}\right)} \]

Where:

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

Explanation: This formula calculates the longest chord within the annulus that is tangent to the inner circle, using the perimeter and outer radius as inputs.

3. Importance of Longest Interval Calculation

Details: Calculating the longest interval of annulus is important in various engineering and geometric applications, particularly in mechanical design, architecture, and spatial analysis where annular shapes are involved.

4. Using the Calculator

Tips: Enter the perimeter of annulus and outer circle radius in meters. Both values must be positive numbers. The calculator will compute the longest interval of the annulus.

5. Frequently Asked Questions (FAQ)

Q1: What is an annulus?
A: An annulus is the region between two concentric circles, resembling a ring or washer shape.

Q2: How is this different from the diameter?
A: The longest interval is the chord tangent to the inner circle, not necessarily passing through the center, while the diameter always passes through the center.

Q3: Can this formula be used for any annulus?
A: Yes, this formula applies to any annulus where the perimeter and outer radius are known.

Q4: What units should be used?
A: Consistent units must be used (preferably meters). The result will be in the same units as the input.

Q5: What if the inner circle is very small?
A: As the inner circle approaches zero radius, the annulus becomes nearly a full circle, and the longest interval approaches the diameter of the outer circle.