Area of Annulus Sector Given Outer Circle Radius and Breadth of Annulus Calculator

Annulus Sector Area Formula:

\[ A_{Sector} = b \times (2 \times r_{Outer} - b) \times \frac{\angle_{Central(Sector)}}{2} \]

Breadth of Annulus (b):

Outer Circle Radius of Annulus (rOuter):

Central Angle of Annulus Sector (∠Central(Sector)):

rad

Area of Annulus Sector (ASector):

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1. What is the Area of Annulus Sector?

The Area of Annulus Sector is the total region covered between the outer and the inner circle of the Annulus Sector. It represents the area of a sector (a portion) of an annulus, which is the ring-shaped region between two concentric circles.

2. How Does the Calculator Work?

The calculator uses the Annulus Sector Area formula:

\[ A_{Sector} = b \times (2 \times r_{Outer} - b) \times \frac{\angle_{Central(Sector)}}{2} \]

Where:

\( b \) — Breadth of Annulus (m)
\( r_{Outer} \) — Outer Circle Radius of Annulus (m)
\( \angle_{Central(Sector)} \) — Central Angle of Annulus Sector (rad)

Explanation: This formula calculates the area of a sector in an annulus by considering the breadth of the annulus, the outer radius, and the central angle of the sector.

3. Importance of Annulus Sector Area Calculation

Details: Calculating the area of an annulus sector is important in various engineering, architectural, and mathematical applications where ring-shaped segments need to be measured or designed, such as in mechanical parts, circular structures, and geometric analysis.

4. Using the Calculator

Tips: Enter the breadth of annulus and outer circle radius in meters, and the central angle in radians. All values must be positive, with the central angle between 0 and 2π (approximately 6.2832) radians.

5. Frequently Asked Questions (FAQ)

Q1: What is an annulus?
A: An annulus is the region between two concentric circles, resembling a ring or washer shape.

Q2: How is the breadth of annulus related to the radii?
A: The breadth of annulus is the difference between the outer and inner radii: \( b = r_{Outer} - r_{Inner} \).

Q3: Can I use degrees instead of radians?
A: The formula requires radians. To convert degrees to radians, multiply by π/180.

Q4: What is the range of valid central angle values?
A: The central angle should be between 0 and 2π radians (0° to 360°).

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the provided formula, assuming precise input values.