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Arc length of cycloid given perimeter Solution

STEP 0: Pre-Calculation Summary
Formula Used
arc_length = 8*(Perimeter/((8+(2*pi))))
s = 8*(P/((8+(2*pi))))
This formula uses 1 Constants, 1 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Perimeter - The perimeter of a figure is the total distance around the edge of the figure. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Perimeter: 20 Meter --> 20 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
s = 8*(P/((8+(2*pi)))) --> 8*(20/((8+(2*pi))))
Evaluating ... ...
s = 11.2019830702311
STEP 3: Convert Result to Output's Unit
11.2019830702311 Meter --> No Conversion Required
FINAL ANSWER
11.2019830702311 Meter <-- Arc Length
(Calculation completed in 00.016 seconds)

11 Other formulas that you can solve using the same Inputs

Diagonal of a Rectangle when breadth and perimeter are given
diagonal = sqrt((2*(Breadth)^2)-(Perimeter*Breadth)+((Perimeter)^2/4)) Go
Diagonal of a Rectangle when length and perimeter are given
diagonal = sqrt((2*(Length)^2)-(Perimeter*Length)+((Perimeter)^2/4)) Go
Area of a Rectangle when breadth and perimeter are given
area = (Perimeter*(Breadth/2))-(Breadth)^2 Go
Area of rectangle when perimeter and breadth are given
area = (Perimeter*Breadth-2*(Breadth)^2)/2 Go
Area of a Rectangle when length and perimeter are given
area = (Perimeter*(Length/2))-(Length)^2 Go
Area of rectangle when perimeter and length are given
area = (Perimeter*Length-2*(Length)^2)/2 Go
Length of rectangle when perimeter and breadth are given
length = (Perimeter-2*Breadth)/2 Go
Breadth of rectangle when perimeter and length are given
breadth = (Perimeter-2*Length)/2 Go
Diagonal of a Square when perimeter is given
diagonal = (Perimeter/4)*sqrt(2) Go
Side of a Kite when other side and perimeter are given
side_a = (Perimeter/2)-Side B Go
Area of a Square when perimeter is given
area = (1/16)*(Perimeter)^2 Go

11 Other formulas that calculate the same Output

Arc length of the circle when central angle and radius are given
arc_length = (pi*Radius*Central Angle)/(180*pi/180) Go
Length of arc when central angle and radius are given
arc_length = (pi*Radius*Central Angle)/(180*pi/180) Go
Arc Length
arc_length = 2*pi*Radius*(Angle A/360) Go
Length of arc when area of quadrant is given
arc_length = 2*pi*(Area/pi)^(0.5) Go
Length of arc when area and corresponding angle are given
arc_length = (Area/pi)*Angle A Go
Arc length from Radius and Arc Angle
arc_length = radius of circle*Subtended Angle in Radians Go
Length of arc when radius and corresponding angle are given
arc_length = Radius*Angle A Go
Arc of a semicircle
arc_length = pi*Radius Go
Length of arc intercepted by tangent chord angle
arc_length = 2*Inscribed Angle Go
Length of arc intercepted by inscribed angle
arc_length = 2*Inscribed Angle Go
Length of arc intercepted by central angle
arc_length = Central Angle Go

Arc length of cycloid given perimeter Formula

arc_length = 8*(Perimeter/((8+(2*pi))))
s = 8*(P/((8+(2*pi))))

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 Arc length of cycloid given perimeter?

Arc length of cycloid given perimeter calculator uses arc_length = 8*(Perimeter/((8+(2*pi)))) to calculate the Arc Length, The Arc length of cycloid given perimeter formula is defined as the distance between two points along a section of a curve, determining the length of an irregular arc segment is also called rectification of a curve, where b = arc length of cycloid, a = radius of cycloid. Arc Length and is denoted by s symbol.

How to calculate Arc length of cycloid given perimeter using this online calculator? To use this online calculator for Arc length of cycloid given perimeter, enter Perimeter (P) and hit the calculate button. Here is how the Arc length of cycloid given perimeter calculation can be explained with given input values -> 11.20198 = 8*(20/((8+(2*pi)))).

FAQ

What is Arc length of cycloid given perimeter?
The Arc length of cycloid given perimeter formula is defined as the distance between two points along a section of a curve, determining the length of an irregular arc segment is also called rectification of a curve, where b = arc length of cycloid, a = radius of cycloid and is represented as s = 8*(P/((8+(2*pi)))) or arc_length = 8*(Perimeter/((8+(2*pi)))). The perimeter of a figure is the total distance around the edge of the figure.
How to calculate Arc length of cycloid given perimeter?
The Arc length of cycloid given perimeter formula is defined as the distance between two points along a section of a curve, determining the length of an irregular arc segment is also called rectification of a curve, where b = arc length of cycloid, a = radius of cycloid is calculated using arc_length = 8*(Perimeter/((8+(2*pi)))). To calculate Arc length of cycloid given perimeter, you need Perimeter (P). With our tool, you need to enter the respective value for Perimeter 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 Arc Length?
In this formula, Arc Length uses Perimeter. We can use 11 other way(s) to calculate the same, which is/are as follows -
  • arc_length = 2*pi*Radius*(Angle A/360)
  • arc_length = (pi*Radius*Central Angle)/(180*pi/180)
  • arc_length = (pi*Radius*Central Angle)/(180*pi/180)
  • arc_length = radius of circle*Subtended Angle in Radians
  • arc_length = pi*Radius
  • arc_length = Central Angle
  • arc_length = 2*Inscribed Angle
  • arc_length = 2*Inscribed Angle
  • arc_length = Radius*Angle A
  • arc_length = 2*pi*(Area/pi)^(0.5)
  • arc_length = (Area/pi)*Angle A
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