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Radius Of Outer Circle Of Annulus Given Inner Circle Radius And Longest Interval Calculator

Formula Used:

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

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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:

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

Where:

Explanation: This formula is derived from the Pythagorean theorem, where the longest interval (chord tangent to the inner circle) forms a right triangle with the radii of the two circles.

3. Importance of Outer Circle Radius Calculation

Details: Calculating the outer circle radius is essential for determining the area of the annulus, understanding geometric properties of concentric circles, and solving various engineering and mathematical problems involving annular shapes.

4. Using the Calculator

Tips: Enter the longest interval of annulus and inner circle radius in meters. Both values must be positive numbers. The calculator will compute the outer circle radius using the geometric relationship between these parameters.

5. Frequently Asked Questions (FAQ)

Q1: What is an annulus?
A: An annulus is a ring-shaped region between two concentric circles, resembling a flat circular ring or washer.

Q2: What is the longest interval of 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 don't intersect the inner circle.

Q3: Can the inner radius be zero?
A: No, if the inner radius were zero, it would simply be a circle, not an annulus. The inner radius must be greater than zero to form a proper annulus.

Q4: What are practical applications of this calculation?
A: This calculation is used in engineering for pipe design, mechanical parts like washers and bearings, architecture for circular structures, and various mathematical applications involving circular geometry.

Q5: How accurate is this formula?
A: This formula is mathematically exact and provides precise results for any valid input values, as it's derived from fundamental geometric principles.

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