Chord Length of Astroid 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 [r_{Fixed Circle}]

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✖A Chord Length of Astroid is a straight line segment whose endpoints both lie on a circular arc of an Astroid.ⓘ Chord Length of Astroid [l_c]

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Chord Length of Astroid Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.

STEP 1: Convert Input(s) to Base Unit

Radius of Fixed Circle of Astroid: 8 Meter --> 8 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_c = 2*r_{Fixed Circle}*sin(pi/4) --> 2*8*sin(pi/4)

Evaluating ... ...

l_c = 11.3137084989848

STEP 3: Convert Result to Output's Unit

11.3137084989848 Meter --> No Conversion Required

FINAL ANSWER

11.3137084989848 ≈ 11.31371 Meter <-- Chord Length of Astroid

(Calculation completed in 00.020 seconds)

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St Joseph's College (SJC), Bengaluru

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Indian Institute of Information Technology (IIIT), Bhopal

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< Chord Length of Astroid Calculators

Chord Length of Astroid given Area

LaTeX Go Chord Length of Astroid = 2*sqrt((8*Area of Astroid)/(3*pi))*sin(pi/4)

Chord Length of Astroid given Radius of Rolling Circle

LaTeX Go Chord Length of Astroid = 8*Radius of Rolling Circle of Astroid*sin(pi/4)

Chord Length of Astroid

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

Chord Length of Astroid given Perimeter

LaTeX Go Chord Length of Astroid = Perimeter of Astroid/3*sin(pi/4)

Chord Length of Astroid Formula

LaTeX Go

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

What is an Astroid?

A 4-cusped Hypocycloid 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 Chord Length of Astroid?

Chord Length of Astroid calculator uses Chord Length of Astroid = 2*Radius of Fixed Circle of Astroid*sin(pi/4) to calculate the Chord Length of Astroid, The Chord Length of Astroid formula is defined as the length of the straight line segment whose both end points lie on the curve of Astroid. Chord Length of Astroid is denoted by l_c symbol.

How to calculate Chord Length of Astroid using this online calculator? To use this online calculator for Chord Length of Astroid, enter Radius of Fixed Circle of Astroid (r_{Fixed Circle}) and hit the calculate button. Here is how the Chord Length of Astroid calculation can be explained with given input values -> 11.31371 = 2*8*sin(pi/4).

FAQ

What is Chord Length of Astroid?

The Chord Length of Astroid formula is defined as the length of the straight line segment whose both end points lie on the curve of Astroid and is represented as l_c = 2*r_{Fixed Circle}*sin(pi/4) or Chord Length of Astroid = 2*Radius of Fixed Circle of Astroid*sin(pi/4). The Radius of Fixed Circle of Astroid is the distance from the center of the fixed circle to any point on its circumference.

How to calculate Chord Length of Astroid?

The Chord Length of Astroid formula is defined as the length of the straight line segment whose both end points lie on the curve of Astroid is calculated using Chord Length of Astroid = 2*Radius of Fixed Circle of Astroid*sin(pi/4). To calculate Chord Length of Astroid, you need Radius of Fixed Circle of Astroid (r_{Fixed Circle}). With our tool, you need to enter the respective value for Radius of Fixed Circle 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 Chord Length of Astroid?

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

Chord Length of Astroid = 2*sqrt((8*Area of Astroid)/(3*pi))*sin(pi/4)
Chord Length of Astroid = Perimeter of Astroid/3*sin(pi/4)
Chord Length of Astroid = 8*Radius of Rolling Circle of Astroid*sin(pi/4)

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