Chord Length of Astroid given Perimeter 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 given Perimeter [l_c]

⎘ Copy

👎

Formula

✖

Chord Length of Astroid given Perimeter

Formula

`"l"_{"c"} = "P"/3*sin(pi/4)`

Example

`"11.78511m"="50m"/3*sin(pi/4)`

Calculator

LaTeX

Reset

👍

Download Astroid Formulas PDF

Chord Length of Astroid given Perimeter Solution

STEP 0: Pre-Calculation Summary

Formula Used

Chord Length of Astroid = Perimeter of Astroid/3*sin(pi/4)
l_c = P/3*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.
Perimeter of Astroid - (Measured in Meter) - The Perimeter of Astroid is a closed path that encompasses, surrounds, or outlines an Astroid.

STEP 1: Convert Input(s) to Base Unit

Perimeter of Astroid: 50 Meter --> 50 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_c = P/3*sin(pi/4) --> 50/3*sin(pi/4)

Evaluating ... ...

l_c = 11.7851130197758

STEP 3: Convert Result to Output's Unit

11.7851130197758 Meter --> No Conversion Required

FINAL ANSWER

11.7851130197758 ≈ 11.78511 Meter <-- Chord Length of Astroid

(Calculation completed in 00.004 seconds)

You are here -

Home » Math » Geometry » 2D Geometry » Astroid » Chord Length of Astroid » Chord Length of Astroid given Perimeter

Credits

Created by Mona Gladys

St Joseph's College (SJC), Bengaluru

Mona Gladys has created this Calculator and 2000+ more calculators!

Verified by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

Mridul Sharma has verified this Calculator and 1700+ more calculators!

< 4 Chord Length of Astroid Calculators

Chord Length of Astroid given Area

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

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

Chord Length of Astroid

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

Chord Length of Astroid given Perimeter

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

Chord Length of Astroid given Perimeter Formula

Chord Length of Astroid = Perimeter of Astroid/3*sin(pi/4)
l_c = P/3*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 Chord Length of Astroid given Perimeter?

Chord Length of Astroid given Perimeter calculator uses Chord Length of Astroid = Perimeter of Astroid/3*sin(pi/4) to calculate the Chord Length of Astroid, The Chord Length of Astroid given Perimeter formula is defined as the length of a straight line segment whose both end points lie on the curve of Astroid, calculated using the perimeter of it. Chord Length of Astroid is denoted by l_c symbol.

How to calculate Chord Length of Astroid given Perimeter using this online calculator? To use this online calculator for Chord Length of Astroid given Perimeter, enter Perimeter of Astroid (P) and hit the calculate button. Here is how the Chord Length of Astroid given Perimeter calculation can be explained with given input values -> 11.78511 = 50/3*sin(pi/4).

FAQ

What is Chord Length of Astroid given Perimeter?

The Chord Length of Astroid given Perimeter formula is defined as the length of a straight line segment whose both end points lie on the curve of Astroid, calculated using the perimeter of it and is represented as l_c = P/3*sin(pi/4) or Chord Length of Astroid = Perimeter of Astroid/3*sin(pi/4). The Perimeter of Astroid is a closed path that encompasses, surrounds, or outlines an Astroid.

How to calculate Chord Length of Astroid given Perimeter?

The Chord Length of Astroid given Perimeter formula is defined as the length of a straight line segment whose both end points lie on the curve of Astroid, calculated using the perimeter of it is calculated using Chord Length of Astroid = Perimeter of Astroid/3*sin(pi/4). To calculate Chord Length of Astroid given Perimeter, you need Perimeter of Astroid (P). With our tool, you need to enter the respective value for Perimeter 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 Perimeter of Astroid. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

Home

FREE PDFs

🔍 Search