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

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

Diagonal of Annulus Sector Example

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Here is how the Diagonal of Annulus Sector equation looks like with Values.

Here is how the Diagonal of Annulus Sector equation looks like with Units.

Here is how the Diagonal of Annulus Sector equation looks like.

5.6637 = \sqrt{10^{2} + 6^{2} - 2 \cdot 10 \cdot 6 \cdot \cos (30)}

5.6637m = \sqrt{{10m}^{2} + {6m}^{2} - 2 \cdot 10m \cdot 6m \cdot \cos (30°)}

5.6637 = \sqrt{10^{2} + 6^{2} - 2 \cdot 10 \cdot 6 \cdot \cos (30)}

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Diagonal of Annulus Sector Solution

Follow our step by step solution on how to calculate Diagonal of Annulus Sector?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

d Sector = \sqrt{{10m}^{2} + {6m}^{2} - 2 \cdot 10m \cdot 6m \cdot \cos (30°)}

Next Step Convert Units

∴

d Sector = \sqrt{{10m}^{2} + {6m}^{2} - 2 \cdot 10m \cdot 6m \cdot \cos (0.5236rad)}

Next Step Prepare to Evaluate

∴

d Sector = \sqrt{10^{2} + 6^{2} - 2 \cdot 10 \cdot 6 \cdot \cos (0.5236)}

Next Step Evaluate

∴

d Sector = 5.66365178536493m

LAST Step Rounding Answer

∴

d Sector = 5.6637m

Diagonal of Annulus Sector 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

Outer Circle Radius of Annulus

Outer Circle Radius of Annulus is the radius of a larger circle of the two concentric circles that form its boundary.

Symbol: r_Outer

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Outer Circle Radius of Annulus

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

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 in Diagonal of Annulus Sector category

Go Area of Annulus Sector

A Sector = ({r Outer}^{2} - {r Inner}^{2}) \cdot \frac{∠ Central(Sector)}{2}

Go Central Angle of Annulus Sector given Inner Arc Length

∠ Central(Sector) = \frac{l Inner Arc(Sector)}{r Inner}

Go Central Angle of Annulus Sector given Outer Arc Length

∠ Central(Sector) = \frac{l Outer Arc(Sector)}{r Outer}

Go Inner Arc Length of Annulus Sector

l Inner Arc(Sector) = r Inner \cdot ∠ Central(Sector)

How to Evaluate Diagonal of Annulus Sector?

Diagonal of Annulus Sector evaluator uses 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)) to evaluate the Diagonal of Annulus Sector, The Diagonal of Annulus Sector formula is defined as a line segment joining the two opposite points, at the maximum distance, on the outer and inner arc. Diagonal of Annulus Sector is denoted by d_Sector symbol.

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

FAQs on Diagonal of Annulus Sector

What is the formula to find Diagonal of Annulus Sector?

The formula of Diagonal of Annulus Sector is expressed as 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)). Here is an example- 5.663652 = sqrt(10^2+6^2-2*10*6*cos(0.5235987755982)).

How to calculate Diagonal of Annulus Sector?

With Outer Circle Radius of Annulus (r_Outer), Inner Circle Radius of Annulus (r_Inner) & Central Angle of Annulus Sector (∠_{Central(Sector)}) we can find Diagonal of Annulus Sector using the formula - 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)). This formula also uses Cosine, Square Root Function function(s).

Can the Diagonal of Annulus Sector be negative?

No, the Diagonal of Annulus Sector, measured in Length cannot be negative.

Which unit is used to measure Diagonal of Annulus Sector?

Diagonal of Annulus Sector 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 can be measured.

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Diagonal of Annulus Sector Formula

Diagonal of Annulus Sector Example

Diagonal of Annulus Sector Solution

Diagonal of Annulus Sector Formula Elements

Other formulas in Diagonal of Annulus Sector category

How to Evaluate Diagonal of Annulus Sector?

FAQs on Diagonal of Annulus Sector

Variable Name