Radius of Fixed Circle of Astroid given Chord Length Calculator

✖The Radius of Fixed Circle of Astroid is the distance from the center of the fixed circle to any point on its circumference.ⓘ Radius of Fixed Circle of Astroid given Chord Length [r_{Fixed Circle}]

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Radius of Fixed Circle of Astroid given Chord Length

Formula

`"r"_{"Fixed Circle"} = "l"_{"c"}/(2*sin(pi/4))`

Example

`"7.778175m"="11m"/(2*sin(pi/4))`

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Radius of Fixed Circle of Astroid given Chord Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of Fixed Circle of Astroid = Chord Length of Astroid/(2*sin(pi/4))
r_{Fixed Circle} = l_c/(2*sin(pi/4))
This formula uses 1 Constants, 1 Functions, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

Variables Used

Radius of Fixed Circle of Astroid - (Measured in Meter) - The Radius of Fixed Circle of Astroid is the distance from the center of the fixed circle to any point on its circumference.
Chord Length of Astroid - (Measured in Meter) - A Chord Length of Astroid is a straight line segment whose endpoints both lie on a circular arc of an Astroid.

STEP 1: Convert Input(s) to Base Unit

Chord Length of Astroid: 11 Meter --> 11 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_{Fixed Circle} = l_c/(2*sin(pi/4)) --> 11/(2*sin(pi/4))

Evaluating ... ...

r_{Fixed Circle} = 7.77817459305202

STEP 3: Convert Result to Output's Unit

7.77817459305202 Meter --> No Conversion Required

FINAL ANSWER

7.77817459305202 ≈ 7.778175 Meter <-- Radius of Fixed Circle of Astroid

(Calculation completed in 00.004 seconds)

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St Joseph's College (SJC), Bengaluru

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< 4 Radius of Fixed Circle of Astroid Calculators

Radius of Fixed Circle of Astroid given Chord Length

Go Radius of Fixed Circle of Astroid = Chord Length of Astroid/(2*sin(pi/4))

Radius of Fixed Circle of Astroid given Area

Go Radius of Fixed Circle of Astroid = sqrt((8*Area of Astroid)/(3*pi))

Radius of Fixed Circle of Astroid

Go Radius of Fixed Circle of Astroid = 4*Radius of Rolling Circle of Astroid

Radius of Fixed Circle of Astroid given Perimeter

Go Radius of Fixed Circle of Astroid = Perimeter of Astroid/6

Radius of Fixed Circle of Astroid given Chord Length Formula

Radius of Fixed Circle of Astroid = Chord Length of Astroid/(2*sin(pi/4))
r_{Fixed Circle} = l_c/(2*sin(pi/4))

What is an Astroid?

A 4-cusped Hypocycloid which is sometimes also called a tetracuspid, cubocycloid, or paracycle. The parametric equations of the Astroid can be obtained by plugging in n=a/b=4 or 4/3 into the equations for a general hypocycloid, giving parametric equations. The Astroid can also be formed as the envelope produced when a line segment is moved with each end on one of a pair of perpendicular axes (e.g., it is the curve enveloped by a ladder sliding against a wall or a garage door with the top corner moving along a vertical track; left figure above). The Astroid is therefore a glissette.

How to Calculate Radius of Fixed Circle of Astroid given Chord Length?

Radius of Fixed Circle of Astroid given Chord Length calculator uses Radius of Fixed Circle of Astroid = Chord Length of Astroid/(2*sin(pi/4)) to calculate the Radius of Fixed Circle of Astroid, The Radius of Fixed Circle of Astroid given Chord Length formula is defined as the length of the straight line from the center to the circumference of an Astroid, calculated using its chord length. Radius of Fixed Circle of Astroid is denoted by r_{Fixed Circle} symbol.

How to calculate Radius of Fixed Circle of Astroid given Chord Length using this online calculator? To use this online calculator for Radius of Fixed Circle of Astroid given Chord Length, enter Chord Length of Astroid (l_c) and hit the calculate button. Here is how the Radius of Fixed Circle of Astroid given Chord Length calculation can be explained with given input values -> 7.778175 = 11/(2*sin(pi/4)).

FAQ

What is Radius of Fixed Circle of Astroid given Chord Length?

The Radius of Fixed Circle of Astroid given Chord Length formula is defined as the length of the straight line from the center to the circumference of an Astroid, calculated using its chord length and is represented as r_{Fixed Circle} = l_c/(2*sin(pi/4)) or Radius of Fixed Circle of Astroid = Chord Length of Astroid/(2*sin(pi/4)). A Chord Length of Astroid is a straight line segment whose endpoints both lie on a circular arc of an Astroid.

How to calculate Radius of Fixed Circle of Astroid given Chord Length?

The Radius of Fixed Circle of Astroid given Chord Length formula is defined as the length of the straight line from the center to the circumference of an Astroid, calculated using its chord length is calculated using Radius of Fixed Circle of Astroid = Chord Length of Astroid/(2*sin(pi/4)). To calculate Radius of Fixed Circle of Astroid given Chord Length, you need Chord Length of Astroid (l_c). With our tool, you need to enter the respective value for Chord Length of Astroid 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 Radius of Fixed Circle of Astroid?

In this formula, Radius of Fixed Circle of Astroid uses Chord Length of Astroid. We can use 3 other way(s) to calculate the same, which is/are as follows -

Radius of Fixed Circle of Astroid = 4*Radius of Rolling Circle of Astroid
Radius of Fixed Circle of Astroid = sqrt((8*Area of Astroid)/(3*pi))
Radius of Fixed Circle of Astroid = Perimeter of Astroid/6

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