Longest interval of Annulus given perimeter and outer circle Solution

STEP 0: Pre-Calculation Summary
Formula Used
Longest interval of Annulus = 2*sqrt((Perimeter of Annulus/(2*pi))*(2*Outer circle radius of Annulus-Perimeter of Annulus/(2*pi)))
l = 2*sqrt((P/(2*pi))*(2*rOuter-P/(2*pi)))
This formula uses 1 Constants, 1 Functions, 3 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sqrt - Squre root function, 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.
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.
STEP 1: Convert Input(s) to Base Unit
Perimeter of Annulus: 100 Meter --> 100 Meter No Conversion Required
Outer circle radius of Annulus: 10 Meter --> 10 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
l = 2*sqrt((P/(2*pi))*(2*rOuter-P/(2*pi))) --> 2*sqrt((100/(2*pi))*(2*10-100/(2*pi)))
Evaluating ... ...
l = 16.1253746719816
STEP 3: Convert Result to Output's Unit
16.1253746719816 Meter --> No Conversion Required
FINAL ANSWER
16.1253746719816 Meter <-- Longest interval of Annulus
(Calculation completed in 00.016 seconds)

Credits

Created by prachi gami
NATIONAL INSTITUTE OF ENGINEERING (nie), mysore
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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
Longest interval of Annulus = 2*sqrt((Perimeter of Annulus/(2*pi))*(Perimeter of Annulus/(2*pi)-2*Inner circle radius of Annulus)) Go
Longest interval of Annulus given perimeter and outer circle
Longest interval of Annulus = 2*sqrt((Perimeter of Annulus/(2*pi))*(2*Outer circle radius of Annulus-Perimeter of Annulus/(2*pi))) Go
Longest interval of Annulus given breadth and inner circle
Longest interval of Annulus = 2*sqrt(Breadth of Annulus*(Breadth of Annulus+2*Inner circle radius of Annulus)) Go
Longest interval of Annulus given breadth and outer circle
Longest interval of Annulus = 2*sqrt(Breadth of Annulus*(2*Outer circle radius of Annulus-Breadth of Annulus)) Go
Longest interval of Annulus given perimeter and breadth
Longest interval of Annulus = 2*sqrt(Perimeter of Annulus*Breadth of Annulus/(2*pi)) Go
Longest interval of Annulus
Longest interval of Annulus = 2*sqrt((Outer circle radius of Annulus^2)-(Inner circle radius of Annulus^2)) Go
Longest interval of Annulus given area
Longest interval of Annulus = 2*sqrt(Area of Annulus/pi) Go

Longest interval of Annulus given perimeter and outer circle Formula

Longest interval of Annulus = 2*sqrt((Perimeter of Annulus/(2*pi))*(2*Outer circle radius of Annulus-Perimeter of Annulus/(2*pi)))
l = 2*sqrt((P/(2*pi))*(2*rOuter-P/(2*pi)))

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 outer circle?

Longest interval of Annulus given perimeter and outer circle calculator uses Longest interval of Annulus = 2*sqrt((Perimeter of Annulus/(2*pi))*(2*Outer circle radius of Annulus-Perimeter of Annulus/(2*pi))) to calculate the Longest interval of Annulus, The Longest interval of Annulus given perimeter and outer circle formula is defined as the length of the longest line segment within the annulus, which is the chord tangent to the inner circle, where l=2*sqrt(R²-r²) , R = radius of outer circle of Annulus, r = radius of inner circle of Annulus, l = longest interval of Annulus, calculated using perimeter and outer circle. Longest interval of Annulus is denoted by l symbol.

How to calculate Longest interval of Annulus given perimeter and outer circle using this online calculator? To use this online calculator for Longest interval of Annulus given perimeter and outer circle, enter Perimeter of Annulus (P) & Outer circle radius of Annulus (rOuter) and hit the calculate button. Here is how the Longest interval of Annulus given perimeter and outer circle calculation can be explained with given input values -> 16.12537 = 2*sqrt((100/(2*pi))*(2*10-100/(2*pi))).

FAQ

What is Longest interval of Annulus given perimeter and outer circle?
The Longest interval of Annulus given perimeter and outer circle formula is defined as the length of the longest line segment within the annulus, which is the chord tangent to the inner circle, where l=2*sqrt(R²-r²) , R = radius of outer circle of Annulus, r = radius of inner circle of Annulus, l = longest interval of Annulus, calculated using perimeter and outer circle and is represented as l = 2*sqrt((P/(2*pi))*(2*rOuter-P/(2*pi))) or Longest interval of Annulus = 2*sqrt((Perimeter of Annulus/(2*pi))*(2*Outer circle radius of Annulus-Perimeter of Annulus/(2*pi))). Perimeter of Annulus is defined as the total distance around the edge of the Annulus & Outer circle Radius of Annulus is the radius of a larger circle of the two concentric circles that form its boundary.
How to calculate Longest interval of Annulus given perimeter and outer circle?
The Longest interval of Annulus given perimeter and outer circle formula is defined as the length of the longest line segment within the annulus, which is the chord tangent to the inner circle, where l=2*sqrt(R²-r²) , R = radius of outer circle of Annulus, r = radius of inner circle of Annulus, l = longest interval of Annulus, calculated using perimeter and outer circle is calculated using Longest interval of Annulus = 2*sqrt((Perimeter of Annulus/(2*pi))*(2*Outer circle radius of Annulus-Perimeter of Annulus/(2*pi))). To calculate Longest interval of Annulus given perimeter and outer circle, you need Perimeter of Annulus (P) & Outer circle radius of Annulus (rOuter). With our tool, you need to enter the respective value for Perimeter of Annulus & Outer 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 & Outer 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))*(Perimeter of Annulus/(2*pi)-2*Inner circle radius of Annulus))
  • 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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