Radius of Fixed Circle 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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✖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 Area [r_{Fixed Circle}]

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Radius of Fixed Circle of Astroid given Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of Fixed Circle of Astroid = sqrt((8*Area of Astroid)/(3*pi))
r_{Fixed Circle} = sqrt((8*A)/(3*pi))
This formula uses 1 Constants, 1 Functions, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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

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.
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

r_{Fixed Circle} = sqrt((8*A)/(3*pi)) --> sqrt((8*75)/(3*pi))

Evaluating ... ...

r_{Fixed Circle} = 7.97884560802865

STEP 3: Convert Result to Output's Unit

7.97884560802865 Meter --> No Conversion Required

FINAL ANSWER

7.97884560802865 ≈ 7.978846 Meter <-- Radius of Fixed Circle of Astroid

(Calculation completed in 00.020 seconds)

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< Radius of Fixed Circle of Astroid Calculators

Radius of Fixed Circle of Astroid given Chord Length

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

Radius of Fixed Circle of Astroid given Area

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

Radius of Fixed Circle of Astroid

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

Radius of Fixed Circle of Astroid given Perimeter

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

Radius of Fixed Circle of Astroid given Area Formula

LaTeX Go

Radius of Fixed Circle of Astroid = sqrt((8*Area of Astroid)/(3*pi))
r_{Fixed Circle} = sqrt((8*A)/(3*pi))

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 Area?

Radius of Fixed Circle of Astroid given Area calculator uses Radius of Fixed Circle of Astroid = sqrt((8*Area of Astroid)/(3*pi)) to calculate the Radius of Fixed Circle of Astroid, The Radius of Fixed Circle of Astroid given Area formula is defined as the straight line from the center to the circumference of an Astroid, calculated using its area. Radius of Fixed Circle of Astroid is denoted by r_{Fixed Circle} symbol.

How to calculate Radius of Fixed Circle of Astroid given Area using this online calculator? To use this online calculator for Radius of Fixed Circle of Astroid given Area, enter Area of Astroid (A) and hit the calculate button. Here is how the Radius of Fixed Circle of Astroid given Area calculation can be explained with given input values -> 7.978846 = sqrt((8*75)/(3*pi)).

FAQ

What is Radius of Fixed Circle of Astroid given Area?

The Radius of Fixed Circle of Astroid given Area formula is defined as the straight line from the center to the circumference of an Astroid, calculated using its area and is represented as r_{Fixed Circle} = sqrt((8*A)/(3*pi)) or Radius of Fixed Circle of Astroid = sqrt((8*Area of Astroid)/(3*pi)). 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 Radius of Fixed Circle of Astroid given Area?

The Radius of Fixed Circle of Astroid given Area formula is defined as the straight line from the center to the circumference of an Astroid, calculated using its area is calculated using Radius of Fixed Circle of Astroid = sqrt((8*Area of Astroid)/(3*pi)). To calculate Radius of Fixed Circle 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 Radius of Fixed Circle of Astroid?

In this formula, Radius of Fixed Circle of Astroid uses Area 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 = Chord Length of Astroid/(2*sin(pi/4))
Radius of Fixed Circle of Astroid = Perimeter of Astroid/6

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