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

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

GoDiagonal of Annulus Sector Formula

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Diagonal of Annulus Sector is a line segment joining the two opposite points, at the maximum distance, on the outer and inner arc. Check FAQs

d Sector = \sqrt{(2 \cdot r Inner \cdot (1 - \cos (∠ Central(Sector))) \cdot (r Inner + b)) + b^{2}}

d_Sector - Diagonal of Annulus Sector?r_Inner - Inner Circle Radius of Annulus?∠_{Central(Sector)} - Central Angle of Annulus Sector?b - Breadth of Annulus?

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

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Here is how the Diagonal of Annulus Sector given Inner Circle Radius and Breadth of Annulus equation looks like with Values.

Here is how the Diagonal of Annulus Sector given Inner Circle Radius and Breadth of Annulus equation looks like with Units.

Here is how the Diagonal of Annulus Sector given Inner Circle Radius and Breadth of Annulus equation looks like.

5.6637 = \sqrt{(2 \cdot 6 \cdot (1 - \cos (30)) \cdot (6 + 4)) + 4^{2}}

5.6637m = \sqrt{(2 \cdot 6m \cdot (1 - \cos (30°)) \cdot (6m + 4m)) + {4m}^{2}}

5.6637 = \sqrt{(2 \cdot 6 \cdot (1 - \cos (30)) \cdot (6 + 4)) + 4^{2}}

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

Follow our step by step solution on how to calculate Diagonal of Annulus Sector given Inner Circle Radius and Breadth of Annulus?

FIRST Step Consider the formula

d Sector = \sqrt{(2 \cdot r Inner \cdot (1 - \cos (∠ Central(Sector))) \cdot (r Inner + b)) + b^{2}}

Next Step Substitute values of Variables

∴

d Sector = \sqrt{(2 \cdot 6m \cdot (1 - \cos (30°)) \cdot (6m + 4m)) + {4m}^{2}}

Next Step Convert Units

∴

d Sector = \sqrt{(2 \cdot 6m \cdot (1 - \cos (0.5236rad)) \cdot (6m + 4m)) + {4m}^{2}}

Next Step Prepare to Evaluate

∴

d Sector = \sqrt{(2 \cdot 6 \cdot (1 - \cos (0.5236)) \cdot (6 + 4)) + 4^{2}}

Next Step Evaluate

∴

d Sector = 5.66365178536493m

LAST Step Rounding Answer

∴

d Sector = 5.6637m

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

Variables

Functions

Diagonal of Annulus Sector

Diagonal of Annulus Sector is a line segment joining the two opposite points, at the maximum distance, on the outer and inner arc.

Symbol: d_Sector

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diagonal of Annulus Sector

Inner Circle Radius of Annulus

Inner Circle Radius of Annulus is the radius of its cavity and it is the smaller radius among two concentric circles.

Symbol: r_Inner

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inner Circle Radius of Annulus

Central Angle of Annulus Sector

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.

Symbol: ∠_{Central(Sector)}

Measurement: AngleUnit: °

Note: Value should be between 0 to 360.

Formulas to find Central Angle of Annulus Sector

Breadth of Annulus

Breadth of Annulus is defined as the shortest distance or measurement between outer circle and inner circle of Annulus.

Symbol: b

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Breadth of Annulus

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: 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.

Syntax: sqrt(Number)

Other Formulas to find Diagonal of Annulus Sector

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

d Sector = \sqrt{(2 \cdot r Outer \cdot (1 - \cos (∠ Central(Sector))) \cdot (r Outer - b)) + b^{2}}

Go Diagonal of Annulus Sector

d Sector = \sqrt{{r Outer}^{2} + {r Inner}^{2} - 2 \cdot r Outer \cdot r Inner \cdot \cos (∠ Central(Sector))}

How to Evaluate Diagonal of Annulus Sector given Inner Circle Radius and Breadth of Annulus?

Diagonal of Annulus Sector given Inner Circle Radius and Breadth of Annulus evaluator uses 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) to evaluate the Diagonal of Annulus Sector, The Diagonal of Annulus Sector given Inner 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 inner circle radius and breadth of Annulus. Diagonal of Annulus Sector is denoted by d_Sector symbol.

How to evaluate Diagonal of Annulus Sector given Inner Circle Radius and Breadth of Annulus using this online evaluator? To use this online evaluator for Diagonal of Annulus Sector given Inner Circle Radius and Breadth of Annulus, enter Inner Circle Radius of Annulus (r_Inner), Central Angle of Annulus Sector (∠_{Central(Sector)}) & Breadth of Annulus (b) and hit the calculate button.

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

What is the formula to find Diagonal of Annulus Sector given Inner Circle Radius and Breadth of Annulus?

The formula of Diagonal of Annulus Sector given Inner Circle Radius and Breadth of Annulus is expressed as 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). Here is an example- 5.663652 = sqrt((2*6*(1-cos(0.5235987755982))*(6+4))+4^2).

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

With Inner Circle Radius of Annulus (r_Inner), Central Angle of Annulus Sector (∠_{Central(Sector)}) & Breadth of Annulus (b) we can find Diagonal of Annulus Sector given Inner Circle Radius and Breadth of Annulus using the formula - 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). This formula also uses Cosine (cos), Square Root (sqrt) function(s).

What are the other ways to Calculate Diagonal of Annulus Sector?

Here are the different ways to Calculate Diagonal of Annulus Sector-

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=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))

Can the Diagonal of Annulus Sector given Inner Circle Radius and Breadth of Annulus be negative?

No, the Diagonal of Annulus Sector given Inner Circle Radius and Breadth of Annulus, measured in Length cannot be negative.

Which unit is used to measure Diagonal of Annulus Sector given Inner Circle Radius and Breadth of Annulus?

Diagonal of Annulus Sector given Inner Circle Radius and Breadth of Annulus is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Diagonal of Annulus Sector given Inner Circle Radius and Breadth of Annulus can be measured.

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

​GoDiagonal of Annulus Sector given Outer Circle Radius and Breadth of Annulus Formula

​GoDiagonal of Annulus Sector Formula

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

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

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

Other Formulas to find Diagonal of Annulus Sector

How to Evaluate Diagonal of Annulus Sector given Inner Circle Radius and Breadth of Annulus?

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

Variable Name

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

GoDiagonal of Annulus Sector Formula