Outer Radius of Circular Ring Given Inner Radius and Longest Interval Calculator

Formula Used:

\[ r_{Outer} = \sqrt{\left(\frac{I_{Longest}}{2}\right)^2 + r_{Inner}^2} \]

Outer Radius of Circular Ring:

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1. What is the Outer Radius of Circular Ring?

The Outer Radius of Circular Ring is the radius of a larger circle of the two concentric circles that form its boundary. It represents the distance from the center to the outer edge of the circular ring.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_{Outer} = \sqrt{\left(\frac{I_{Longest}}{2}\right)^2 + r_{Inner}^2} \]

Where:

\( r_{Outer} \) — Outer Radius of Circular Ring (m)
\( I_{Longest} \) — Longest Interval of Circular Ring (m)
\( r_{Inner} \) — Inner Radius of Circular Ring (m)

Explanation: This formula calculates the outer radius using the Pythagorean theorem, where the longest interval forms the base of a right triangle with the inner and outer radii.

3. Importance of Outer Radius Calculation

Details: Calculating the outer radius is essential for determining the complete dimensions of circular rings, which is crucial in engineering, architecture, and various manufacturing applications involving annular shapes.

4. Using the Calculator

Tips: Enter the longest interval and inner radius in meters. Both values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a circular ring?
A: A circular ring is the region between two concentric circles - an annulus formed by two circles sharing the same center but with different radii.

Q2: What does the longest interval represent?
A: The longest interval is the chord tangent to the inner circle, which represents the maximum distance between two points on the outer circumference that doesn't cross the inner circle.

Q3: Can this formula be used for elliptical rings?
A: No, this formula is specifically for circular rings with concentric circles. Elliptical rings require different geometric calculations.

Q4: What are the practical applications of this calculation?
A: This calculation is used in pipe design, bearing manufacturing, architectural elements, and any application involving annular shapes where complete dimensional analysis is required.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect circular rings. The accuracy in practical applications depends on the precision of the input measurements.