Chord Length of Astroid given Area Calculator

✖Area of Astroid is defined as measure of the total area or region occupied by an Astroid within its four concave sides or boundaries.ⓘ Area of Astroid [A]

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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 given Area [l_c]

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Formula

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Chord Length of Astroid given Area

Formula

`"l"_{"c"} = 2*sqrt((8*"A")/(3*pi))*sin(pi/4)`

Example

`"11.28379m"=2*sqrt((8*"75m²")/(3*pi))*sin(pi/4)`

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Chord Length of Astroid given Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Chord Length of Astroid = 2*sqrt((8*Area of Astroid)/(3*pi))*sin(pi/4)
l_c = 2*sqrt((8*A)/(3*pi))*sin(pi/4)
This formula uses 1 Constants, 2 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)
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

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.
Area of Astroid - (Measured in Square Meter) - Area of Astroid is defined as measure of the total area or region occupied by an Astroid within its four concave sides or boundaries.

STEP 1: Convert Input(s) to Base Unit

Area of Astroid: 75 Square Meter --> 75 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_c = 2*sqrt((8*A)/(3*pi))*sin(pi/4) --> 2*sqrt((8*75)/(3*pi))*sin(pi/4)

Evaluating ... ...

l_c = 11.2837916709551

STEP 3: Convert Result to Output's Unit

11.2837916709551 Meter --> No Conversion Required

FINAL ANSWER

11.2837916709551 ≈ 11.28379 Meter <-- Chord Length of Astroid

(Calculation completed in 00.004 seconds)

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< 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 Area Formula

Chord Length of Astroid = 2*sqrt((8*Area of Astroid)/(3*pi))*sin(pi/4)
l_c = 2*sqrt((8*A)/(3*pi))*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 given Area?

Chord Length of Astroid given Area calculator uses Chord Length of Astroid = 2*sqrt((8*Area of Astroid)/(3*pi))*sin(pi/4) to calculate the Chord Length of Astroid, The Chord Length of Astroid given Area formula is defined as the length of straight line segment whose both end points lie on the curve of Astroid, calculated using area of it. Chord Length of Astroid is denoted by l_c symbol.

How to calculate Chord Length of Astroid given Area using this online calculator? To use this online calculator for Chord Length of Astroid given Area, enter Area of Astroid (A) and hit the calculate button. Here is how the Chord Length of Astroid given Area calculation can be explained with given input values -> 11.28379 = 2*sqrt((8*75)/(3*pi))*sin(pi/4).

FAQ

What is Chord Length of Astroid given Area?

The Chord Length of Astroid given Area formula is defined as the length of straight line segment whose both end points lie on the curve of Astroid, calculated using area of it and is represented as l_c = 2*sqrt((8*A)/(3*pi))*sin(pi/4) or Chord Length of Astroid = 2*sqrt((8*Area of Astroid)/(3*pi))*sin(pi/4). Area of Astroid is defined as measure of the total area or region occupied by an Astroid within its four concave sides or boundaries.

How to calculate Chord Length of Astroid given Area?

The Chord Length of Astroid given Area formula is defined as the length of straight line segment whose both end points lie on the curve of Astroid, calculated using area of it is calculated using Chord Length of Astroid = 2*sqrt((8*Area of Astroid)/(3*pi))*sin(pi/4). To calculate Chord Length of Astroid given Area, you need Area of Astroid (A). With our tool, you need to enter the respective value for Area 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 Area 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 = 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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