Central Angle of Annulus Sector given Diagonal 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%
✖Inner Circle Radius of Annulus is the radius of its cavity and it is the smaller radius among two concentric circles.ⓘ Inner Circle Radius of Annulus [r_Inner]			+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 [d_Sector]			+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 Diagonal [∠_{Central(Sector)}]

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Central Angle of Annulus Sector given Diagonal Solution

STEP 0: Pre-Calculation Summary

Formula Used

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(Sector)} = acos((r_Outer^2+r_Inner^2-d_Sector^2)/(2*r_Outer*r_Inner))
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.
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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Outer Circle Radius of Annulus: 10 Meter --> 10 Meter No Conversion Required
Inner Circle Radius of Annulus: 6 Meter --> 6 Meter No Conversion Required
Diagonal of Annulus Sector: 7 Meter --> 7 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

∠_{Central(Sector)} = acos((r_Outer^2+r_Inner^2-d_Sector^2)/(2*r_Outer*r_Inner)) --> acos((10^2+6^2-7^2)/(2*10*6))

Evaluating ... ...

∠_{Central(Sector)} = 0.759761932507315

STEP 3: Convert Result to Output's Unit

0.759761932507315 Radian -->43.5311521673806 Degree (Check conversion here)

FINAL ANSWER

43.5311521673806 ≈ 43.53115 Degree <-- Central Angle of Annulus Sector

(Calculation completed in 00.020 seconds)

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Mumbai University (DJSCE), Mumbai

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< Central Angle of Annulus Sector Calculators

Central Angle of Annulus Sector given Perimeter

LaTeX 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 Area

LaTeX 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

LaTeX 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

LaTeX 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 Diagonal Formula

LaTeX Go

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?

Central Angle of Annulus Sector given Diagonal calculator uses 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)) to calculate the Central Angle of Annulus Sector, The Central Angle of Annulus Sector given Diagonal 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 of Annulus Sector. Central Angle of Annulus Sector is denoted by ∠_{Central(Sector)} symbol.

How to calculate Central Angle of Annulus Sector given Diagonal using this online calculator? To use this online calculator for Central Angle of Annulus Sector given Diagonal, enter Outer Circle Radius of Annulus (r_Outer), Inner Circle Radius of Annulus (r_Inner) & Diagonal of Annulus Sector (d_Sector) and hit the calculate button. Here is how the Central Angle of Annulus Sector given Diagonal calculation can be explained with given input values -> 2494.151 = acos((10^2+6^2-7^2)/(2*10*6)).

FAQ

What is Central Angle of Annulus Sector given Diagonal?

The Central Angle of Annulus Sector given Diagonal 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 of Annulus Sector and is represented as ∠_{Central(Sector)} = acos((r_Outer^2+r_Inner^2-d_Sector^2)/(2*r_Outer*r_Inner)) or 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)). Outer Circle Radius of Annulus is the radius of a larger circle of the two concentric circles that form its boundary, Inner Circle Radius of Annulus is the radius of its cavity and it is the smaller radius among two concentric circles & Diagonal of Annulus Sector is a line segment joining the two opposite points, at the maximum distance, on the outer and inner arc.

How to calculate Central Angle of Annulus Sector given Diagonal?

The Central Angle of Annulus Sector given Diagonal 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 of Annulus Sector is calculated using 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)). To calculate Central Angle of Annulus Sector given Diagonal, you need Outer Circle Radius of Annulus (r_Outer), Inner Circle Radius of Annulus (r_Inner) & Diagonal of Annulus Sector (d_Sector). With our tool, you need to enter the respective value for Outer Circle Radius of Annulus, Inner Circle Radius of Annulus & Diagonal of Annulus Sector 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 Outer Circle Radius of Annulus, Inner Circle Radius of Annulus & Diagonal of Annulus Sector. We can use 3 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)

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