Area of Astroid given Radius of Rolling Circle Calculator

✖Radius of Rolling Circle of Astroid is the distance from the center of the rolling circle to any point on its circumference.ⓘ Radius of Rolling Circle of Astroid [r_{Rolling 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 given Radius of Rolling Circle [A]

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Area of Astroid given Radius of Rolling Circle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Astroid = 3/8*pi*(4*Radius of Rolling Circle of Astroid)^2
A = 3/8*pi*(4*r_{Rolling 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 Rolling Circle of Astroid - (Measured in Meter) - Radius of Rolling Circle of Astroid is the distance from the center of the rolling circle to any point on its circumference.

STEP 1: Convert Input(s) to Base Unit

Radius of Rolling Circle of Astroid: 2 Meter --> 2 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = 3/8*pi*(4*r_{Rolling circle})^2 --> 3/8*pi*(4*2)^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 00.020 seconds)

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St Joseph's College (SJC), Bengaluru

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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 given Radius of Rolling Circle Formula

LaTeX Go

Area of Astroid = 3/8*pi*(4*Radius of Rolling Circle of Astroid)^2
A = 3/8*pi*(4*r_{Rolling 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 given Radius of Rolling Circle?

Area of Astroid given Radius of Rolling Circle calculator uses Area of Astroid = 3/8*pi*(4*Radius of Rolling Circle of Astroid)^2 to calculate the Area of Astroid, The Area of Astroid given Radius of Rolling Circle formula is defined as the measure of the total space enclosed inside the Astroid, calculated using the radius of the rolling circle. Area of Astroid is denoted by A symbol.

How to calculate Area of Astroid given Radius of Rolling Circle using this online calculator? To use this online calculator for Area of Astroid given Radius of Rolling Circle, enter Radius of Rolling Circle of Astroid (r_{Rolling circle}) and hit the calculate button. Here is how the Area of Astroid given Radius of Rolling Circle calculation can be explained with given input values -> 75.39822 = 3/8*pi*(4*2)^2.

FAQ

What is Area of Astroid given Radius of Rolling Circle?

The Area of Astroid given Radius of Rolling Circle formula is defined as the measure of the total space enclosed inside the Astroid, calculated using the radius of the rolling circle and is represented as A = 3/8*pi*(4*r_{Rolling circle})^2 or Area of Astroid = 3/8*pi*(4*Radius of Rolling Circle of Astroid)^2. Radius of Rolling Circle of Astroid is the distance from the center of the rolling circle to any point on its circumference.

How to calculate Area of Astroid given Radius of Rolling Circle?

The Area of Astroid given Radius of Rolling Circle formula is defined as the measure of the total space enclosed inside the Astroid, calculated using the radius of the rolling circle is calculated using Area of Astroid = 3/8*pi*(4*Radius of Rolling Circle of Astroid)^2. To calculate Area of Astroid given Radius of Rolling Circle, you need Radius of Rolling Circle of Astroid (r_{Rolling circle}). With our tool, you need to enter the respective value for Radius of Rolling 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 Rolling 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*Radius of Fixed Circle of Astroid^2
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

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