Area of Cycloid given Arc Length Calculator

✖Arc Length of Cycloid is the distance between two points along a section of a curve.ⓘ Arc Length of Cycloid [l_Arc]

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✖The Area of Cycloid is the amount of two-dimensional space taken up by the Cycloid.ⓘ Area of Cycloid given Arc Length [A]

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Area of Cycloid given Arc Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Cycloid = 3*pi*(Arc Length of Cycloid/8)^2
A = 3*pi*(l_Arc/8)^2
This formula uses 1 Constants, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Area of Cycloid - (Measured in Square Meter) - The Area of Cycloid is the amount of two-dimensional space taken up by the Cycloid.
Arc Length of Cycloid - (Measured in Meter) - Arc Length of Cycloid is the distance between two points along a section of a curve.

STEP 1: Convert Input(s) to Base Unit

Arc Length of Cycloid: 40 Meter --> 40 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = 3*pi*(l_Arc/8)^2 --> 3*pi*(40/8)^2

Evaluating ... ...

A = 235.619449019234

STEP 3: Convert Result to Output's Unit

235.619449019234 Square Meter --> No Conversion Required

FINAL ANSWER

235.619449019234 ≈ 235.6194 Square Meter <-- Area of Cycloid

(Calculation completed in 00.004 seconds)

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St Joseph's College (SJC), Bengaluru

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< Area of Cycloid Calculators

Area of Cycloid given Base Length

LaTeX Go Area of Cycloid = 3*pi*(Base Length of Cycloid/(2*pi))^2

Area of Cycloid

LaTeX Go Area of Cycloid = 3*pi*Radius of Circle of Cycloid^2

Area of Cycloid given Arc Length

LaTeX Go Area of Cycloid = 3*pi*(Arc Length of Cycloid/8)^2

Area of Cycloid given Height

LaTeX Go Area of Cycloid = 3*pi*(Height of Cycloid/2)^2

Area of Cycloid given Arc Length Formula

LaTeX Go

Area of Cycloid = 3*pi*(Arc Length of Cycloid/8)^2
A = 3*pi*(l_Arc/8)^2

What is a Cycloid?

In geometry, a Cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping. A cycloid is a specific form of trochoid and is an example of a roulette, a curve generated by a curve rolling on another curve. The cycloid, with the cusps pointing upward, is the curve of fastest descent under constant gravity (the brachistochrone curve). It is also the form of a curve for which the period of an object in simple harmonic motion (rolling up and down repetitively) along the curve does not depend on the object's starting position (the tautochrone curve).

How to Calculate Area of Cycloid given Arc Length?

Area of Cycloid given Arc Length calculator uses Area of Cycloid = 3*pi*(Arc Length of Cycloid/8)^2 to calculate the Area of Cycloid, The Area of Cycloid given Arc Length formula is defined as the measure of the total 2-D space that the surface of the object occupies of a Cycloid, calculated using its arc length. Area of Cycloid is denoted by A symbol.

How to calculate Area of Cycloid given Arc Length using this online calculator? To use this online calculator for Area of Cycloid given Arc Length, enter Arc Length of Cycloid (l_Arc) and hit the calculate button. Here is how the Area of Cycloid given Arc Length calculation can be explained with given input values -> 235.6194 = 3*pi*(40/8)^2.

FAQ

What is Area of Cycloid given Arc Length?

The Area of Cycloid given Arc Length formula is defined as the measure of the total 2-D space that the surface of the object occupies of a Cycloid, calculated using its arc length and is represented as A = 3*pi*(l_Arc/8)^2 or Area of Cycloid = 3*pi*(Arc Length of Cycloid/8)^2. Arc Length of Cycloid is the distance between two points along a section of a curve.

How to calculate Area of Cycloid given Arc Length?

The Area of Cycloid given Arc Length formula is defined as the measure of the total 2-D space that the surface of the object occupies of a Cycloid, calculated using its arc length is calculated using Area of Cycloid = 3*pi*(Arc Length of Cycloid/8)^2. To calculate Area of Cycloid given Arc Length, you need Arc Length of Cycloid (l_Arc). With our tool, you need to enter the respective value for Arc Length of Cycloid 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 Cycloid?

In this formula, Area of Cycloid uses Arc Length of Cycloid. We can use 3 other way(s) to calculate the same, which is/are as follows -

Area of Cycloid = 3*pi*Radius of Circle of Cycloid^2
Area of Cycloid = 3*pi*(Base Length of Cycloid/(2*pi))^2
Area of Cycloid = 3*pi*(Height of Cycloid/2)^2

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