Radius of Outer Circle of Annulus given Area and Perimeter Calculator

Formula Used:

\[ r_{Outer} = \frac{\frac{P}{2\pi} + \frac{\frac{A}{\pi}}{\frac{P}{2\pi}}}{2} \]

Outer Circle Radius:

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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 the annulus. It represents the distance from the center to the outer edge of the ring-shaped figure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_{Outer} = \frac{\frac{P}{2\pi} + \frac{\frac{A}{\pi}}{\frac{P}{2\pi}}}{2} \]

Where:

\( r_{Outer} \) — Outer Circle Radius of Annulus (m)
\( P \) — Perimeter of Annulus (m)
\( A \) — Area of Annulus (m²)
\( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: This formula calculates the outer radius by combining information about both the perimeter and area of the annulus, providing an accurate measurement of the larger circle's radius.

3. Importance of Outer Circle Radius Calculation

Details: Calculating the outer radius is essential in various engineering and design applications, particularly in mechanical engineering, architecture, and manufacturing where annular shapes are common.

4. Using the Calculator

Tips: Enter the perimeter and area of the annulus in meters and square meters respectively. Both values must be positive numbers for accurate calculation.

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 this different from calculating the inner radius?
A: The inner radius would be calculated differently, typically using the formula: \( r_{Inner} = \sqrt{r_{Outer}^2 - \frac{A}{\pi}} \).

Q3: What are practical applications of this calculation?
A: This calculation is used in designing pipes, washers, bearings, and any circular components with hollow centers.

Q4: What units should I use?
A: The calculator uses meters for length and square meters for area, but you can use any consistent unit system as long as you're consistent.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect annular shapes. Real-world measurements may have slight variations due to manufacturing tolerances.