Perimeter of Astroid given Chord Length Calculator

✖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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✖The Perimeter of Astroid is a closed path that encompasses, surrounds, or outlines an Astroid.ⓘ Perimeter of Astroid given Chord Length [P]

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Perimeter of Astroid given Chord Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

Perimeter of Astroid = 6*(Chord Length of Astroid/(2*sin(pi/4)))
P = 6*(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

Perimeter of Astroid - (Measured in Meter) - The Perimeter of Astroid is a closed path that encompasses, surrounds, or outlines an Astroid.
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

P = 6*(l_c/(2*sin(pi/4))) --> 6*(11/(2*sin(pi/4)))

Evaluating ... ...

P = 46.6690475583121

STEP 3: Convert Result to Output's Unit

46.6690475583121 Meter --> No Conversion Required

FINAL ANSWER

46.6690475583121 ≈ 46.66905 Meter <-- Perimeter 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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< Perimeter of Astroid Calculators

Perimeter of Astroid given Chord Length

LaTeX Go Perimeter of Astroid = 6*(Chord Length of Astroid/(2*sin(pi/4)))

Perimeter of Astroid given Area

LaTeX Go Perimeter of Astroid = 6*sqrt((8*Area of Astroid)/(3*pi))

Perimeter of Astroid given Radius of Rolling Circle

LaTeX Go Perimeter of Astroid = 24*Radius of Rolling Circle of Astroid

Perimeter of Astroid

LaTeX Go Perimeter of Astroid = 6*Radius of Fixed Circle of Astroid

Perimeter of Astroid given Chord Length Formula

LaTeX Go

Perimeter of Astroid = 6*(Chord Length of Astroid/(2*sin(pi/4)))
P = 6*(l_c/(2*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 Perimeter of Astroid given Chord Length?

Perimeter of Astroid given Chord Length calculator uses Perimeter of Astroid = 6*(Chord Length of Astroid/(2*sin(pi/4))) to calculate the Perimeter of Astroid, The Perimeter of Astroid given Chord Length formula is defined as the outermost parts or boundary of a concave pentagon. Perimeter of Astroid is denoted by P symbol.

How to calculate Perimeter of Astroid given Chord Length using this online calculator? To use this online calculator for Perimeter of Astroid given Chord Length, enter Chord Length of Astroid (l_c) and hit the calculate button. Here is how the Perimeter of Astroid given Chord Length calculation can be explained with given input values -> 46.66905 = 6*(11/(2*sin(pi/4))).

FAQ

What is Perimeter of Astroid given Chord Length?

The Perimeter of Astroid given Chord Length formula is defined as the outermost parts or boundary of a concave pentagon and is represented as P = 6*(l_c/(2*sin(pi/4))) or Perimeter of Astroid = 6*(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 Perimeter of Astroid given Chord Length?

The Perimeter of Astroid given Chord Length formula is defined as the outermost parts or boundary of a concave pentagon is calculated using Perimeter of Astroid = 6*(Chord Length of Astroid/(2*sin(pi/4))). To calculate Perimeter 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 Perimeter of Astroid?

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

Perimeter of Astroid = 6*Radius of Fixed Circle of Astroid
Perimeter of Astroid = 24*Radius of Rolling Circle of Astroid
Perimeter of Astroid = 6*sqrt((8*Area of Astroid)/(3*pi))

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