Longest Interval of Annulus given Perimeter and Inner Circle Radius Calculator

✖Perimeter of Annulus is defined as the total distance around the edge of the Annulus.ⓘ Perimeter of Annulus [P]			+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%

✖Longest Interval of Annulus is the length of the longest line segment within the Annulus, which is the chord tangent to the inner circle.ⓘ Longest Interval of Annulus given Perimeter and Inner Circle Radius [l]

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Formula

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Longest Interval of Annulus given Perimeter and Inner Circle Radius

Formula

`"l" = 2*sqrt("P"/(2*pi)*("P"/(2*pi)-(2*"r"_{"Inner"})))`

Example

`"15.78823m"=2*sqrt("100m"/(2*pi)*("100m"/(2*pi)-(2*"6m")))`

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Longest Interval of Annulus given Perimeter and Inner Circle Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Longest Interval of Annulus = 2*sqrt(Perimeter of Annulus/(2*pi)*(Perimeter of Annulus/(2*pi)-(2*Inner Circle Radius of Annulus)))
l = 2*sqrt(P/(2*pi)*(P/(2*pi)-(2*r_Inner)))
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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

Longest Interval of Annulus - (Measured in Meter) - Longest Interval of Annulus is the length of the longest line segment within the Annulus, which is the chord tangent to the inner circle.
Perimeter of Annulus - (Measured in Meter) - Perimeter of Annulus is defined as the total distance around the edge of the 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

Perimeter of Annulus: 100 Meter --> 100 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

l = 2*sqrt(P/(2*pi)*(P/(2*pi)-(2*r_Inner))) --> 2*sqrt(100/(2*pi)*(100/(2*pi)-(2*6)))

Evaluating ... ...

l = 15.7882269296549

STEP 3: Convert Result to Output's Unit

15.7882269296549 Meter --> No Conversion Required

FINAL ANSWER

15.7882269296549 ≈ 15.78823 Meter <-- Longest Interval of Annulus

(Calculation completed in 00.004 seconds)

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Created by prachi gami

NATIONAL INSTITUTE OF ENGINEERING (nie), mysore

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Verified by Nikita Kumari

The National Institute of Engineering (NIE), Mysuru

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< 7 Longest Interval of Annulus Calculators

Longest Interval of Annulus given Perimeter and Inner Circle Radius

Go Longest Interval of Annulus = 2*sqrt(Perimeter of Annulus/(2*pi)*(Perimeter of Annulus/(2*pi)-(2*Inner Circle Radius of Annulus)))

Longest Interval of Annulus given Perimeter and Outer Circle Radius

Go Longest Interval of Annulus = 2*sqrt(Perimeter of Annulus/(2*pi)*((2*Outer Circle Radius of Annulus)-Perimeter of Annulus/(2*pi)))

Longest Interval of Annulus given Breadth and Inner Circle Radius

Go Longest Interval of Annulus = 2*sqrt(Breadth of Annulus*(Breadth of Annulus+2*Inner Circle Radius of Annulus))

Longest Interval of Annulus given Breadth and Outer Circle Radius

Go Longest Interval of Annulus = 2*sqrt(Breadth of Annulus*(2*Outer Circle Radius of Annulus-Breadth of Annulus))

Longest Interval of Annulus given Perimeter and Breadth

Go Longest Interval of Annulus = 2*sqrt(Perimeter of Annulus*Breadth of Annulus/(2*pi))

Longest Interval of Annulus

Go Longest Interval of Annulus = 2*sqrt(Outer Circle Radius of Annulus^2-Inner Circle Radius of Annulus^2)

Longest Interval of Annulus given Area

Go Longest Interval of Annulus = 2*sqrt(Area of Annulus/pi)

Longest Interval of Annulus given Perimeter and Inner Circle Radius Formula

Longest Interval of Annulus = 2*sqrt(Perimeter of Annulus/(2*pi)*(Perimeter of Annulus/(2*pi)-(2*Inner Circle Radius of Annulus)))
l = 2*sqrt(P/(2*pi)*(P/(2*pi)-(2*r_Inner)))

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 Longest Interval of Annulus given Perimeter and Inner Circle Radius?

Longest Interval of Annulus given Perimeter and Inner Circle Radius calculator uses Longest Interval of Annulus = 2*sqrt(Perimeter of Annulus/(2*pi)*(Perimeter of Annulus/(2*pi)-(2*Inner Circle Radius of Annulus))) to calculate the Longest Interval of Annulus, The Longest Interval of Annulus given Perimeter and Inner Circle Radius formula is defined as the length of the longest line segment within the Annulus, which is the chord tangent to the inner circle, calculated using perimeter and inner circle radius. Longest Interval of Annulus is denoted by l symbol.

How to calculate Longest Interval of Annulus given Perimeter and Inner Circle Radius using this online calculator? To use this online calculator for Longest Interval of Annulus given Perimeter and Inner Circle Radius, enter Perimeter of Annulus (P) & Inner Circle Radius of Annulus (r_Inner) and hit the calculate button. Here is how the Longest Interval of Annulus given Perimeter and Inner Circle Radius calculation can be explained with given input values -> 15.78823 = 2*sqrt(100/(2*pi)*(100/(2*pi)-(2*6))).

FAQ

What is Longest Interval of Annulus given Perimeter and Inner Circle Radius?

The Longest Interval of Annulus given Perimeter and Inner Circle Radius formula is defined as the length of the longest line segment within the Annulus, which is the chord tangent to the inner circle, calculated using perimeter and inner circle radius and is represented as l = 2*sqrt(P/(2*pi)*(P/(2*pi)-(2*r_Inner))) or Longest Interval of Annulus = 2*sqrt(Perimeter of Annulus/(2*pi)*(Perimeter of Annulus/(2*pi)-(2*Inner Circle Radius of Annulus))). Perimeter of Annulus is defined as the total distance around the edge of the Annulus & Inner Circle Radius of Annulus is the radius of its cavity and it is the smaller radius among two concentric circles.

How to calculate Longest Interval of Annulus given Perimeter and Inner Circle Radius?

The Longest Interval of Annulus given Perimeter and Inner Circle Radius formula is defined as the length of the longest line segment within the Annulus, which is the chord tangent to the inner circle, calculated using perimeter and inner circle radius is calculated using Longest Interval of Annulus = 2*sqrt(Perimeter of Annulus/(2*pi)*(Perimeter of Annulus/(2*pi)-(2*Inner Circle Radius of Annulus))). To calculate Longest Interval of Annulus given Perimeter and Inner Circle Radius, you need Perimeter of Annulus (P) & Inner Circle Radius of Annulus (r_Inner). With our tool, you need to enter the respective value for Perimeter of Annulus & Inner Circle Radius 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 Longest Interval of Annulus?

In this formula, Longest Interval of Annulus uses Perimeter of Annulus & Inner Circle Radius of Annulus. We can use 6 other way(s) to calculate the same, which is/are as follows -

Longest Interval of Annulus = 2*sqrt(Outer Circle Radius of Annulus^2-Inner Circle Radius of Annulus^2)
Longest Interval of Annulus = 2*sqrt(Area of Annulus/pi)
Longest Interval of Annulus = 2*sqrt(Perimeter of Annulus/(2*pi)*((2*Outer Circle Radius of Annulus)-Perimeter of Annulus/(2*pi)))
Longest Interval of Annulus = 2*sqrt(Breadth of Annulus*(Breadth of Annulus+2*Inner Circle Radius of Annulus))
Longest Interval of Annulus = 2*sqrt(Breadth of Annulus*(2*Outer Circle Radius of Annulus-Breadth of Annulus))
Longest Interval of Annulus = 2*sqrt(Perimeter of Annulus*Breadth of Annulus/(2*pi))

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