Central Angle of Annulus Sector given Area and Outer Circle Radius Calculator

✖Area of Annulus Sector is the total region covered between the outer and the inner circle of the Annulus Sector.ⓘ Area of Annulus Sector [A_Sector]			+10% -10%
✖Breadth of Annulus is defined as the shortest distance or measurement between outer circle and inner circle of Annulus.ⓘ Breadth of Annulus [b]			+10% -10%
✖Outer Circle Radius of Annulus is the radius of a larger circle of the two concentric circles that form its boundary.ⓘ Outer Circle Radius of Annulus [r_Outer]			+10% -10%

✖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.ⓘ Central Angle of Annulus Sector given Area and Outer Circle Radius [∠_{Central(Sector)}]

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Formula

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Central Angle of Annulus Sector given Area and Outer Circle Radius

Formula

`"∠"_{"Central(Sector)"} = (2*"A"_{"Sector"})/("b"*((2*"r"_{"Outer"})-"b"))`

Example

`"26.8574°"=(2*"15m²")/("4m"*((2*"10m")-"4m"))`

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Central Angle of Annulus Sector given Area and Outer Circle Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Central Angle of Annulus Sector = (2*Area of Annulus Sector)/(Breadth of Annulus*((2*Outer Circle Radius of Annulus)-Breadth of Annulus))
∠_{Central(Sector)} = (2*A_Sector)/(b*((2*r_Outer)-b))
This formula uses 4 Variables

Variables Used

Central Angle of Annulus Sector - (Measured in Radian) - 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.
Area of Annulus Sector - (Measured in Square Meter) - Area of Annulus Sector is the total region covered between the outer and the inner circle of the Annulus Sector.
Breadth of Annulus - (Measured in Meter) - Breadth of Annulus is defined as the shortest distance or measurement between outer circle and inner circle of Annulus.
Outer Circle Radius of Annulus - (Measured in Meter) - Outer Circle Radius of Annulus is the radius of a larger circle of the two concentric circles that form its boundary.

STEP 1: Convert Input(s) to Base Unit

Area of Annulus Sector: 15 Square Meter --> 15 Square Meter No Conversion Required
Breadth of Annulus: 4 Meter --> 4 Meter No Conversion Required
Outer Circle Radius of Annulus: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

∠_{Central(Sector)} = (2*A_Sector)/(b*((2*r_Outer)-b)) --> (2*15)/(4*((2*10)-4))

Evaluating ... ...

∠_{Central(Sector)} = 0.46875

STEP 3: Convert Result to Output's Unit

0.46875 Radian -->26.8573966467624 Degree (Check conversion here)

FINAL ANSWER

26.8573966467624 ≈ 26.8574 Degree <-- Central Angle of Annulus Sector

(Calculation completed in 00.004 seconds)

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Home » Math » Geometry » 2D Geometry » Annulus » Sector of Annulus » Central Angle of Annulus Sector » Central Angle of Annulus Sector given Area and Outer Circle Radius

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Created by Nikhil

Mumbai University (DJSCE), Mumbai

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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

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< 13 Central Angle of Annulus Sector Calculators

Central Angle of Annulus Sector given Diagonal

Go Central Angle of Annulus Sector = acos((Outer Circle Radius of Annulus^2+Inner Circle Radius of Annulus^2-Diagonal of Annulus Sector^2)/(2*Outer Circle Radius of Annulus*Inner Circle Radius of Annulus))

Central Angle of Annulus Sector given Diagonal and Inner Circle Radius

Go Central Angle of Annulus Sector = acos(1-((Diagonal of Annulus Sector^2-Breadth of Annulus^2)/(2*Inner Circle Radius of Annulus*(Inner Circle Radius of Annulus+Breadth of Annulus))))

Central Angle of Annulus Sector given Diagonal and Outer Circle Radius

Go Central Angle of Annulus Sector = acos(1-((Diagonal of Annulus Sector^2-Breadth of Annulus^2)/(2*Outer Circle Radius of Annulus*(Outer Circle Radius of Annulus-Breadth of Annulus))))

Central Angle of Annulus Sector given Perimeter

Go Central Angle of Annulus Sector = (Perimeter of Annulus Sector-(2*(Outer Circle Radius of Annulus-Inner Circle Radius of Annulus)))/(Outer Circle Radius of Annulus+Inner Circle Radius of Annulus)

Central Angle of Annulus Sector given Perimeter and Inner Circle Radius

Go Central Angle of Annulus Sector = (Perimeter of Annulus Sector-(2*Breadth of Annulus))/((2*Inner Circle Radius of Annulus)+Breadth of Annulus)

Central Angle of Annulus Sector given Perimeter and Outer Circle Radius

Go Central Angle of Annulus Sector = (Perimeter of Annulus Sector-(2*Breadth of Annulus))/((2*Outer Circle Radius of Annulus)-Breadth of Annulus)

Central Angle of Annulus Sector given Area and Outer Circle Radius

Go Central Angle of Annulus Sector = (2*Area of Annulus Sector)/(Breadth of Annulus*((2*Outer Circle Radius of Annulus)-Breadth of Annulus))

Central Angle of Annulus Sector given Area and Inner Circle Radius

Go Central Angle of Annulus Sector = (2*Area of Annulus Sector)/(Breadth of Annulus*((2*Inner Circle Radius of Annulus)+Breadth of Annulus))

Central Angle of Annulus Sector given Area

Go Central Angle of Annulus Sector = (2*Area of Annulus Sector)/(Outer Circle Radius of Annulus^2-Inner Circle Radius of Annulus^2)

Central Angle of Annulus Sector given Outer Arc Length and Breadth

Go Central Angle of Annulus Sector = Outer Arc Length of Annulus Sector/(Inner Circle Radius of Annulus+Breadth of Annulus)

Central Angle of Annulus Sector given Inner Arc Length and Breadth

Go Central Angle of Annulus Sector = Inner Arc Length of Annulus Sector/(Outer Circle Radius of Annulus-Breadth of Annulus)

Central Angle of Annulus Sector given Outer Arc Length

Go Central Angle of Annulus Sector = Outer Arc Length of Annulus Sector/Outer Circle Radius of Annulus

Central Angle of Annulus Sector given Inner Arc Length

Go Central Angle of Annulus Sector = Inner Arc Length of Annulus Sector/Inner Circle Radius of Annulus

Central Angle of Annulus Sector given Area and Outer Circle Radius Formula

Central Angle of Annulus Sector = (2*Area of Annulus Sector)/(Breadth of Annulus*((2*Outer Circle Radius of Annulus)-Breadth of Annulus))
∠_{Central(Sector)} = (2*A_Sector)/(b*((2*r_Outer)-b))

What is an Annulus Sector?

An Annulus Sector, also known as the circular ring sector, is a cut piece from an Annulus that is joined by two straight lines from its center.

What is Annulus?

In mathematics, an Annulus (plural Annuli or Annuluses) is the region between two concentric circles. Informally, it is shaped like a ring or a hardware washer. The word "annulus" is borrowed from the Latin word anulus or annulus meaning 'little ring'. The adjectival form is annular (as in annular eclipse).The area of an Annulus is the difference in the areas of the larger circle of radius R and the smaller one of radius r.

How to Calculate Central Angle of Annulus Sector given Area and Outer Circle Radius?

Central Angle of Annulus Sector given Area and Outer Circle Radius calculator uses Central Angle of Annulus Sector = (2*Area of Annulus Sector)/(Breadth of Annulus*((2*Outer Circle Radius of Annulus)-Breadth of Annulus)) to calculate the Central Angle of Annulus Sector, Central Angle of Annulus Sector given Area and Outer Circle Radius formula is defined as 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, calculated using area, outer circle radius and breadth of Annulus Sector. Central Angle of Annulus Sector is denoted by ∠_{Central(Sector)} symbol.

How to calculate Central Angle of Annulus Sector given Area and Outer Circle Radius using this online calculator? To use this online calculator for Central Angle of Annulus Sector given Area and Outer Circle Radius, enter Area of Annulus Sector (A_Sector), Breadth of Annulus (b) & Outer Circle Radius of Annulus (r_Outer) and hit the calculate button. Here is how the Central Angle of Annulus Sector given Area and Outer Circle Radius calculation can be explained with given input values -> 1538.815 = (2*15)/(4*((2*10)-4)).

FAQ

What is Central Angle of Annulus Sector given Area and Outer Circle Radius?

Central Angle of Annulus Sector given Area and Outer Circle Radius formula is defined as 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, calculated using area, outer circle radius and breadth of Annulus Sector and is represented as ∠_{Central(Sector)} = (2*A_Sector)/(b*((2*r_Outer)-b)) or Central Angle of Annulus Sector = (2*Area of Annulus Sector)/(Breadth of Annulus*((2*Outer Circle Radius of Annulus)-Breadth of Annulus)). Area of Annulus Sector is the total region covered between the outer and the inner circle of the Annulus Sector, Breadth of Annulus is defined as the shortest distance or measurement between outer circle and inner circle of Annulus & Outer Circle Radius of Annulus is the radius of a larger circle of the two concentric circles that form its boundary.

How to calculate Central Angle of Annulus Sector given Area and Outer Circle Radius?

Central Angle of Annulus Sector given Area and Outer Circle Radius formula is defined as 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, calculated using area, outer circle radius and breadth of Annulus Sector is calculated using Central Angle of Annulus Sector = (2*Area of Annulus Sector)/(Breadth of Annulus*((2*Outer Circle Radius of Annulus)-Breadth of Annulus)). To calculate Central Angle of Annulus Sector given Area and Outer Circle Radius, you need Area of Annulus Sector (A_Sector), Breadth of Annulus (b) & Outer Circle Radius of Annulus (r_Outer). With our tool, you need to enter the respective value for Area of Annulus Sector, Breadth of Annulus & Outer Circle Radius of Annulus and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Central Angle of Annulus Sector?

In this formula, Central Angle of Annulus Sector uses Area of Annulus Sector, Breadth of Annulus & Outer Circle Radius of Annulus. We can use 12 other way(s) to calculate the same, which is/are as follows -

Central Angle of Annulus Sector = (2*Area of Annulus Sector)/(Outer Circle Radius of Annulus^2-Inner Circle Radius of Annulus^2)
Central Angle of Annulus Sector = Outer Arc Length of Annulus Sector/(Inner Circle Radius of Annulus+Breadth of Annulus)
Central Angle of Annulus Sector = Inner Arc Length of Annulus Sector/(Outer Circle Radius of Annulus-Breadth of Annulus)
Central Angle of Annulus Sector = (Perimeter of Annulus Sector-(2*(Outer Circle Radius of Annulus-Inner Circle Radius of Annulus)))/(Outer Circle Radius of Annulus+Inner Circle Radius of Annulus)
Central Angle of Annulus Sector = (2*Area of Annulus Sector)/(Breadth of Annulus*((2*Inner Circle Radius of Annulus)+Breadth of Annulus))
Central Angle of Annulus Sector = (Perimeter of Annulus Sector-(2*Breadth of Annulus))/((2*Inner Circle Radius of Annulus)+Breadth of Annulus)
Central Angle of Annulus Sector = (Perimeter of Annulus Sector-(2*Breadth of Annulus))/((2*Outer Circle Radius of Annulus)-Breadth of Annulus)
Central Angle of Annulus Sector = acos((Outer Circle Radius of Annulus^2+Inner Circle Radius of Annulus^2-Diagonal of Annulus Sector^2)/(2*Outer Circle Radius of Annulus*Inner Circle Radius of Annulus))
Central Angle of Annulus Sector = acos(1-((Diagonal of Annulus Sector^2-Breadth of Annulus^2)/(2*Inner Circle Radius of Annulus*(Inner Circle Radius of Annulus+Breadth of Annulus))))
Central Angle of Annulus Sector = acos(1-((Diagonal of Annulus Sector^2-Breadth of Annulus^2)/(2*Outer Circle Radius of Annulus*(Outer Circle Radius of Annulus-Breadth of Annulus))))
Central Angle of Annulus Sector = Outer Arc Length of Annulus Sector/Outer Circle Radius of Annulus
Central Angle of Annulus Sector = Inner Arc Length of Annulus Sector/Inner Circle Radius of Annulus

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