Diagonal of Annulus Sector given Outer Circle Radius and Breadth of Annulus Calculator

✖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 [∠_{Central(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%

✖Diagonal of Annulus Sector is a line segment joining the two opposite points, at the maximum distance, on the outer and inner arc.ⓘ Diagonal of Annulus Sector given Outer Circle Radius and Breadth of Annulus [d_Sector]

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Formula

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Diagonal of Annulus Sector given Outer Circle Radius and Breadth of Annulus

Formula

`"d"_{"Sector"} = sqrt((2*"r"_{"Outer"}*(1-cos("∠"_{"Central(Sector)"}))*("r"_{"Outer"}-"b"))+"b"^2)`

Example

`"5.663652m"=sqrt((2*"10m"*(1-cos("30°"))*("10m"-"4m"))+("4m")^2)`

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Diagonal of Annulus Sector given Outer Circle Radius and Breadth of Annulus Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diagonal of Annulus Sector = sqrt((2*Outer Circle Radius of Annulus*(1-cos(Central Angle of Annulus Sector))*(Outer Circle Radius of Annulus-Breadth of Annulus))+Breadth of Annulus^2)
d_Sector = sqrt((2*r_Outer*(1-cos(∠_{Central(Sector)}))*(r_Outer-b))+b^2)
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)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

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.
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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Outer Circle Radius of Annulus: 10 Meter --> 10 Meter No Conversion Required
Central Angle of Annulus Sector: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
Breadth of Annulus: 4 Meter --> 4 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_Sector = sqrt((2*r_Outer*(1-cos(∠_{Central(Sector)}))*(r_Outer-b))+b^2) --> sqrt((2*10*(1-cos(0.5235987755982))*(10-4))+4^2)

Evaluating ... ...

d_Sector = 5.66365178536493

STEP 3: Convert Result to Output's Unit

5.66365178536493 Meter --> No Conversion Required

FINAL ANSWER

5.66365178536493 ≈ 5.663652 Meter <-- Diagonal of Annulus Sector

(Calculation completed in 00.020 seconds)

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Home » Math » Geometry » 2D Geometry » Annulus » Sector of Annulus » Diagonal of Annulus Sector » Diagonal of Annulus Sector given Outer Circle Radius and Breadth of Annulus

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< 3 Diagonal of Annulus Sector Calculators

Diagonal of Annulus Sector

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

Diagonal of Annulus Sector given Inner Circle Radius and Breadth of Annulus

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

Diagonal of Annulus Sector given Outer Circle Radius and Breadth of Annulus

Go Diagonal of Annulus Sector = sqrt((2*Outer Circle Radius of Annulus*(1-cos(Central Angle of Annulus Sector))*(Outer Circle Radius of Annulus-Breadth of Annulus))+Breadth of Annulus^2)

Diagonal of Annulus Sector given Outer Circle Radius and Breadth of Annulus Formula

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 Diagonal of Annulus Sector given Outer Circle Radius and Breadth of Annulus?

Diagonal of Annulus Sector given Outer Circle Radius and Breadth of Annulus calculator uses Diagonal of Annulus Sector = sqrt((2*Outer Circle Radius of Annulus*(1-cos(Central Angle of Annulus Sector))*(Outer Circle Radius of Annulus-Breadth of Annulus))+Breadth of Annulus^2) to calculate the Diagonal of Annulus Sector, The Diagonal of Annulus Sector given Outer Circle Radius and Breadth of Annulus formula is defined as a line segment joining the two opposite points, at the maximum distance, on the outer and inner arc, calculated using outer circle radius and breadth of Annulus. Diagonal of Annulus Sector is denoted by d_Sector symbol.

How to calculate Diagonal of Annulus Sector given Outer Circle Radius and Breadth of Annulus using this online calculator? To use this online calculator for Diagonal of Annulus Sector given Outer Circle Radius and Breadth of Annulus, enter Outer Circle Radius of Annulus (r_Outer), Central Angle of Annulus Sector (∠_{Central(Sector)}) & Breadth of Annulus (b) and hit the calculate button. Here is how the Diagonal of Annulus Sector given Outer Circle Radius and Breadth of Annulus calculation can be explained with given input values -> 5.663652 = sqrt((2*10*(1-cos(0.5235987755982))*(10-4))+4^2).

FAQ

What is Diagonal of Annulus Sector given Outer Circle Radius and Breadth of Annulus?

The Diagonal of Annulus Sector given Outer Circle Radius and Breadth of Annulus formula is defined as a line segment joining the two opposite points, at the maximum distance, on the outer and inner arc, calculated using outer circle radius and breadth of Annulus and is represented as d_Sector = sqrt((2*r_Outer*(1-cos(∠_{Central(Sector)}))*(r_Outer-b))+b^2) or Diagonal of Annulus Sector = sqrt((2*Outer Circle Radius of Annulus*(1-cos(Central Angle of Annulus Sector))*(Outer Circle Radius of Annulus-Breadth of Annulus))+Breadth of Annulus^2). Outer Circle Radius of Annulus is the radius of a larger circle of the two concentric circles that form its boundary, 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 & Breadth of Annulus is defined as the shortest distance or measurement between outer circle and inner circle of Annulus.

How to calculate Diagonal of Annulus Sector given Outer Circle Radius and Breadth of Annulus?

The Diagonal of Annulus Sector given Outer Circle Radius and Breadth of Annulus formula is defined as a line segment joining the two opposite points, at the maximum distance, on the outer and inner arc, calculated using outer circle radius and breadth of Annulus is calculated using Diagonal of Annulus Sector = sqrt((2*Outer Circle Radius of Annulus*(1-cos(Central Angle of Annulus Sector))*(Outer Circle Radius of Annulus-Breadth of Annulus))+Breadth of Annulus^2). To calculate Diagonal of Annulus Sector given Outer Circle Radius and Breadth of Annulus, you need Outer Circle Radius of Annulus (r_Outer), Central Angle of Annulus Sector (∠_{Central(Sector)}) & Breadth of Annulus (b). With our tool, you need to enter the respective value for Outer Circle Radius of Annulus, Central Angle of Annulus Sector & Breadth 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 Diagonal of Annulus Sector?

In this formula, Diagonal of Annulus Sector uses Outer Circle Radius of Annulus, Central Angle of Annulus Sector & Breadth of Annulus. We can use 2 other way(s) to calculate the same, which is/are as follows -

Diagonal of Annulus Sector = sqrt((2*Inner Circle Radius of Annulus*(1-cos(Central Angle of Annulus Sector))*(Inner Circle Radius of Annulus+Breadth of Annulus))+Breadth of Annulus^2)
Diagonal of Annulus Sector = sqrt(Outer Circle Radius of Annulus^2+Inner Circle Radius of Annulus^2-2*Outer Circle Radius of Annulus*Inner Circle Radius of Annulus*cos(Central Angle of Annulus Sector))

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