Longest Interval Of Annulus Given Perimeter And Breadth Calculator

Formula Used:

\[ Longest\ Interval\ of\ Annulus = 2 \times \sqrt{\frac{Perimeter\ of\ Annulus \times Breadth\ of\ Annulus}{2 \times \pi}} \]

Longest Interval of Annulus:

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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 passes through the annulus.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l = 2 \times \sqrt{\frac{P \times b}{2 \times \pi}} \]

Where:

\( l \) — Longest Interval of Annulus (m)
\( P \) — Perimeter of Annulus (m)
\( b \) — Breadth of Annulus (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: This formula calculates the longest chord that can be drawn through the annulus, which is tangent to the inner circle, using the perimeter and breadth of the annulus.

3. Importance of Longest Interval Calculation

Details: Calculating the longest interval of an annulus is important in various engineering and geometric applications, particularly in mechanical design, architecture, and material science where annular shapes are used.

4. Using the Calculator

Tips: Enter the perimeter and breadth of the annulus 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 a ring-shaped object, the region bounded by two concentric circles.

Q2: How is the longest interval related to the annulus?
A: The longest interval is the chord of the outer circle that is tangent to the inner circle, representing the maximum distance between two points on the outer circle that passes through the annulus.

Q3: What units should I use for the inputs?
A: The calculator uses meters for both perimeter and breadth, but any consistent unit system can be used as long as both inputs are in the same units.

Q4: Can this formula be used for any annulus?
A: Yes, this formula applies to any annular shape where the inner and outer circles are concentric.

Q5: What if my annulus has different units?
A: Ensure both perimeter and breadth are in the same units before calculation. The result will be in the same units as the inputs.