## Central Angle of Annulus Sector given Diagonal and Inner Circle Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Central(Sector) = acos(1-((dSector^2-b^2)/(2*rInner*(rInner+b))))
This formula uses 2 Functions, 4 Variables
Functions Used
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
acos - The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., acos(Number)
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.
Diagonal of Annulus Sector - (Measured in Meter) - Diagonal of Annulus Sector is a line segment joining the two opposite points, at the maximum distance, on the outer and inner arc.
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.
Inner Circle Radius of Annulus - (Measured in Meter) - Inner Circle Radius of Annulus is the radius of its cavity and it is the smaller radius among two concentric circles.
STEP 1: Convert Input(s) to Base Unit
Diagonal of Annulus Sector: 7 Meter --> 7 Meter No Conversion Required
Breadth of Annulus: 4 Meter --> 4 Meter No Conversion Required
Inner Circle Radius of Annulus: 6 Meter --> 6 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Central(Sector) = acos(1-((dSector^2-b^2)/(2*rInner*(rInner+b)))) --> acos(1-((7^2-4^2)/(2*6*(6+4))))
Evaluating ... ...
Central(Sector) = 0.759761932507315
STEP 3: Convert Result to Output's Unit
0.759761932507315 Radian -->43.5311521673806 Degree (Check conversion ​here)
43.5311521673806 43.53115 Degree <-- Central Angle of Annulus Sector
(Calculation completed in 00.004 seconds)
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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
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
Central Angle of Annulus Sector given Diagonal and Outer Circle Radius
Central Angle of Annulus Sector given Perimeter
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
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
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
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
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
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
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
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
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
Central Angle of Annulus Sector = Inner Arc Length of Annulus Sector/Inner Circle Radius of Annulus

## Central Angle of Annulus Sector given Diagonal and Inner Circle Radius Formula

Central(Sector) = acos(1-((dSector^2-b^2)/(2*rInner*(rInner+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 Diagonal and Inner Circle Radius?

Central Angle of Annulus Sector given Diagonal and Inner Circle Radius calculator uses 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)))) to calculate the Central Angle of Annulus Sector, The Central Angle of Annulus Sector given Diagonal and Inner 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 diagonal, inner 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 Diagonal and Inner Circle Radius using this online calculator? To use this online calculator for Central Angle of Annulus Sector given Diagonal and Inner Circle Radius, enter Diagonal of Annulus Sector (dSector), Breadth of Annulus (b) & Inner Circle Radius of Annulus (rInner) and hit the calculate button. Here is how the Central Angle of Annulus Sector given Diagonal and Inner Circle Radius calculation can be explained with given input values -> 2494.151 = acos(1-((7^2-4^2)/(2*6*(6+4)))).

### FAQ

What is Central Angle of Annulus Sector given Diagonal and Inner Circle Radius?
How to calculate Central Angle of Annulus Sector given Diagonal and Inner Circle Radius?
How many ways are there to calculate Central Angle of Annulus Sector?
In this formula, Central Angle of Annulus Sector uses Diagonal of Annulus Sector, Breadth of Annulus & Inner 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*Outer Circle Radius of Annulus)-Breadth 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*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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