Area 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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✖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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Area of Astroid Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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.
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

A = 3/8*pi*r_{Fixed Circle}^2 --> 3/8*pi*8^2

Evaluating ... ...

A = 75.398223686155

STEP 3: Convert Result to Output's Unit

75.398223686155 Square Meter --> No Conversion Required

FINAL ANSWER

75.398223686155 ≈ 75.39822 Square Meter <-- Area of Astroid

(Calculation completed in 00.004 seconds)

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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

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< Area of Astroid Calculators

Area of Astroid given Chord Length

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

Area of Astroid given Radius of Rolling Circle

LaTeX Go Area of Astroid = 3/8*pi*(4*Radius of Rolling Circle of Astroid)^2

Area of Astroid

LaTeX Go Area of Astroid = 3/8*pi*Radius of Fixed Circle of Astroid^2

Area of Astroid given Perimeter

LaTeX Go Area of Astroid = 3/8*pi*(Perimeter of Astroid/6)^2

Area of Astroid Formula

LaTeX Go

Area of Astroid = 3/8*pi*Radius of Fixed Circle of Astroid^2
A = 3/8*pi*r_{Fixed Circle}^2

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 Area of Astroid?

Area of Astroid calculator uses Area of Astroid = 3/8*pi*Radius of Fixed Circle of Astroid^2 to calculate the Area of Astroid, The Area of Astroid formula is defined as a measure of the total area that the surface of the object occupies of a concave pentagon. Area of Astroid is denoted by A symbol.

How to calculate Area of Astroid using this online calculator? To use this online calculator for Area of Astroid, enter Radius of Fixed Circle of Astroid (r_{Fixed Circle}) and hit the calculate button. Here is how the Area of Astroid calculation can be explained with given input values -> 75.39822 = 3/8*pi*8^2.

FAQ

What is Area of Astroid?

The Area of Astroid formula is defined as a measure of the total area that the surface of the object occupies of a concave pentagon and is represented as A = 3/8*pi*r_{Fixed Circle}^2 or Area of Astroid = 3/8*pi*Radius of Fixed Circle of Astroid^2. 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 Area of Astroid?

The Area of Astroid formula is defined as a measure of the total area that the surface of the object occupies of a concave pentagon is calculated using Area of Astroid = 3/8*pi*Radius of Fixed Circle of Astroid^2. To calculate Area 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 Area of Astroid?

In this formula, Area 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 -

Area of Astroid = 3/8*pi*(Chord Length of Astroid/(2*sin(pi/4)))^2
Area of Astroid = 3/8*pi*(Perimeter of Astroid/6)^2
Area of Astroid = 3/8*pi*(4*Radius of Rolling Circle of Astroid)^2

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