Radius of Inner Circle of Annulus given Outer Circle Radius and Longest Interval 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%
✖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 [l]			+10% -10%

✖Inner Circle Radius of Annulus is the radius of its cavity and it is the smaller radius among two concentric circles.ⓘ Radius of Inner Circle of Annulus given Outer Circle Radius and Longest Interval [r_Inner]

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Formula

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Radius of Inner Circle of Annulus given Outer Circle Radius and Longest Interval

Formula

`"r"_{"Inner"} = sqrt("r"_{"Outer"}^2-("l"/2)^2)`

Example

`"6m"=sqrt(("10m")^2-("16m"/2)^2)`

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Radius of Inner Circle of Annulus given Outer Circle Radius and Longest Interval Solution

STEP 0: Pre-Calculation Summary

Formula Used

Inner Circle Radius of Annulus = sqrt(Outer Circle Radius of Annulus^2-(Longest Interval of Annulus/2)^2)
r_Inner = sqrt(r_Outer^2-(l/2)^2)
This formula uses 1 Functions, 3 Variables

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

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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Outer Circle Radius of Annulus: 10 Meter --> 10 Meter No Conversion Required
Longest Interval of Annulus: 16 Meter --> 16 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_Inner = sqrt(r_Outer^2-(l/2)^2) --> sqrt(10^2-(16/2)^2)

Evaluating ... ...

r_Inner = 6

STEP 3: Convert Result to Output's Unit

6 Meter --> No Conversion Required

FINAL ANSWER

6 Meter <-- Inner Circle Radius of Annulus

(Calculation completed in 00.020 seconds)

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Created by Mona Gladys

St Joseph's College (SJC), Bengaluru

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Walchand College of Engineering (WCE), Sangli

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< 9 Radius of Inner Circle of Annulus Calculators

Radius of Inner Circle of Annulus given Area and Perimeter

Go Inner Circle Radius of Annulus = ((Perimeter of Annulus/(2*pi))-(((Area of Annulus/pi))/((Perimeter of Annulus/(2*pi)))))/2

Radius of Inner Circle of Annulus given Longest Interval and Perimeter

Go Inner Circle Radius of Annulus = ((Perimeter of Annulus/(2*pi))-(((Longest Interval of Annulus^2/4))/((Perimeter of Annulus/(2*pi)))))/2

Radius of Inner Circle of Annulus given Area and Breadth

Go Inner Circle Radius of Annulus = ((((Area of Annulus/pi))/Breadth of Annulus)-Breadth of Annulus)/2

Radius of Inner Circle of Annulus given Outer Circle Radius and Area

Go Inner Circle Radius of Annulus = sqrt(Outer Circle Radius of Annulus^2-Area of Annulus/pi)

Radius of Inner Circle of Annulus given Longest Interval and Breadth

Go Inner Circle Radius of Annulus = ((((Longest Interval of Annulus^2/4))/Breadth of Annulus)-Breadth of Annulus)/2

Radius of Inner Circle of Annulus given Outer Circle Radius and Longest Interval

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

Radius of Inner Circle of Annulus given Outer Circle Radius and Perimeter

Go Inner Circle Radius of Annulus = Perimeter of Annulus/(2*pi)-Outer Circle Radius of Annulus

Radius of Inner Circle of Annulus given Perimeter and Breadth

Go Inner Circle Radius of Annulus = (Perimeter of Annulus/(2*pi)-Breadth of Annulus)/2

Radius of Inner Circle of Annulus given Outer Circle Radius and Breadth

Go Inner Circle Radius of Annulus = Outer Circle Radius of Annulus-Breadth of Annulus

Radius of Inner Circle of Annulus given Outer Circle Radius and Longest Interval Formula

Inner Circle Radius of Annulus = sqrt(Outer Circle Radius of Annulus^2-(Longest Interval of Annulus/2)^2)
r_Inner = sqrt(r_Outer^2-(l/2)^2)

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 Radius of Inner Circle of Annulus given Outer Circle Radius and Longest Interval?

Radius of Inner Circle of Annulus given Outer Circle Radius and Longest Interval calculator uses Inner Circle Radius of Annulus = sqrt(Outer Circle Radius of Annulus^2-(Longest Interval of Annulus/2)^2) to calculate the Inner Circle Radius of Annulus, The Radius of Inner Circle of Annulus given Outer Circle Radius and Longest Interval formula is defined as straight line from Centre to the inner circumference of Annulus, calculated using outer circle radius and longest interval. Inner Circle Radius of Annulus is denoted by r_Inner symbol.

How to calculate Radius of Inner Circle of Annulus given Outer Circle Radius and Longest Interval using this online calculator? To use this online calculator for Radius of Inner Circle of Annulus given Outer Circle Radius and Longest Interval, enter Outer Circle Radius of Annulus (r_Outer) & Longest Interval of Annulus (l) and hit the calculate button. Here is how the Radius of Inner Circle of Annulus given Outer Circle Radius and Longest Interval calculation can be explained with given input values -> 6 = sqrt(10^2-(16/2)^2).

FAQ

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

The Radius of Inner Circle of Annulus given Outer Circle Radius and Longest Interval formula is defined as straight line from Centre to the inner circumference of Annulus, calculated using outer circle radius and longest interval and is represented as r_Inner = sqrt(r_Outer^2-(l/2)^2) or Inner Circle Radius of Annulus = sqrt(Outer Circle Radius of Annulus^2-(Longest Interval of Annulus/2)^2). Outer Circle Radius of Annulus is the radius of a larger circle of the two concentric circles that form its boundary & Longest Interval of Annulus is the length of the longest line segment within the Annulus, which is the chord tangent to the inner circle.

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

The Radius of Inner Circle of Annulus given Outer Circle Radius and Longest Interval formula is defined as straight line from Centre to the inner circumference of Annulus, calculated using outer circle radius and longest interval is calculated using Inner Circle Radius of Annulus = sqrt(Outer Circle Radius of Annulus^2-(Longest Interval of Annulus/2)^2). To calculate Radius of Inner Circle of Annulus given Outer Circle Radius and Longest Interval, you need Outer Circle Radius of Annulus (r_Outer) & Longest Interval of Annulus (l). With our tool, you need to enter the respective value for Outer Circle Radius of Annulus & Longest Interval 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 Inner Circle Radius of Annulus?

In this formula, Inner Circle Radius of Annulus uses Outer Circle Radius of Annulus & Longest Interval of Annulus. We can use 8 other way(s) to calculate the same, which is/are as follows -

Inner Circle Radius of Annulus = Outer Circle Radius of Annulus-Breadth of Annulus
Inner Circle Radius of Annulus = Perimeter of Annulus/(2*pi)-Outer Circle Radius of Annulus
Inner Circle Radius of Annulus = sqrt(Outer Circle Radius of Annulus^2-Area of Annulus/pi)
Inner Circle Radius of Annulus = (Perimeter of Annulus/(2*pi)-Breadth of Annulus)/2
Inner Circle Radius of Annulus = ((((Area of Annulus/pi))/Breadth of Annulus)-Breadth of Annulus)/2
Inner Circle Radius of Annulus = ((((Longest Interval of Annulus^2/4))/Breadth of Annulus)-Breadth of Annulus)/2
Inner Circle Radius of Annulus = ((Perimeter of Annulus/(2*pi))-(((Longest Interval of Annulus^2/4))/((Perimeter of Annulus/(2*pi)))))/2
Inner Circle Radius of Annulus = ((Perimeter of Annulus/(2*pi))-(((Area of Annulus/pi))/((Perimeter of Annulus/(2*pi)))))/2

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