Central Angle of Annulus Sector given Area Calculator

Formula Used:

\[ \text{Central Angle of Annulus Sector} = \frac{2 \times \text{Area of Annulus Sector}}{\text{Outer Circle Radius of Annulus}^2 - \text{Inner Circle Radius of Annulus}^2} \]

Central Angle of Annulus Sector:

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1. What is the Central Angle of Annulus Sector?

The Central Angle of Annulus Sector is the angle whose apex (vertex) is the center of the concentric circles of Annulus and whose legs (sides) are radii intersecting the circles in four distinct points.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Central Angle of Annulus Sector} = \frac{2 \times \text{Area of Annulus Sector}}{\text{Outer Circle Radius of Annulus}^2 - \text{Inner Circle Radius of Annulus}^2} \]

Where:

Area of Annulus Sector — The total region covered between the outer and the inner circle of the Annulus Sector (m²)
Outer Circle Radius of Annulus — The radius of a larger circle of the two concentric circles that form its boundary (m)
Inner Circle Radius of Annulus — The radius of its cavity and it is the smaller radius among two concentric circles (m)

Explanation: This formula calculates the central angle based on the area of the annulus sector and the difference of squares of the outer and inner radii.

3. Importance of Central Angle Calculation

Details: Calculating the central angle is important in geometry and engineering applications where annular sectors are involved, such as in mechanical design, architecture, and various mathematical computations involving circular segments.

4. Using the Calculator

Tips: Enter the area of annulus sector in square meters, outer circle radius in meters, and inner circle radius in meters. All values must be positive, and the outer radius must be greater than the inner radius.

5. Frequently Asked Questions (FAQ)

Q1: What is an annulus sector?
A: An annulus sector is the region between two concentric circles bounded by two radii and their intercepted arcs.

Q2: What units should I use for the inputs?
A: The calculator uses meters for radius measurements and square meters for area. Ensure consistent units for accurate results.

Q3: Can the central angle be greater than 2π radians?
A: Yes, the central angle can be any positive real number, though typically in geometric contexts it's between 0 and 2π radians.

Q4: What if the inner radius is larger than the outer radius?
A: The calculator requires the outer radius to be greater than the inner radius. If this condition is not met, the calculation will not proceed.

Q5: How precise are the results?
A: The results are rounded to 4 decimal places for clarity, but the underlying calculation uses the full precision of the input values.