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

Annulus Sector Area Formula:

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

Breadth of Annulus (b):

Inner Circle Radius of Annulus (r_Inner):

Central Angle of Annulus Sector (∠_{Central(Sector)}):

rad

Area of Annulus Sector (A_Sector):

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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 specific angular section of an annulus (ring-shaped region between two concentric circles).

2. How Does the Calculator Work?

The calculator uses the Annulus Sector Area formula:

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

Where:

\( A_{Sector} \) — Area of Annulus Sector (m²)
\( b \) — Breadth of Annulus (m)
\( r_{Inner} \) — Inner Circle Radius of Annulus (m)
\( \angle_{Central(Sector)} \) — Central Angle of Annulus Sector (radians)

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

3. Importance of Annulus Sector Area Calculation

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

4. Using the Calculator

Tips: Enter the breadth of annulus in meters, inner circle radius in meters, and central angle in radians. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is an annulus?
A: An annulus is the ring-shaped region between two concentric circles - the area between a larger circle and a smaller circle inside it.

Q2: How is this different from regular circle sector area?
A: A regular circle sector is from a single circle, while an annulus sector is the area between two concentric circles within a specific angle.

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

Q4: What if I know the outer radius instead of inner radius?
A: The inner radius can be calculated as outer radius minus breadth (r_Inner = r_Outer - b).

Q5: Are there practical applications of this calculation?
A: Yes, this calculation is used in engineering for designing gears, washers, pipes, and in architecture for circular structures with ring-shaped elements.