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Perimeter of hypocycloid Solution

STEP 0: Pre-Calculation Summary
Formula Used
perimeter = (8*Radius 1*(Number of cusps-1))/Number of cusps
P = (8*r1*(n-1))/n
This formula uses 2 Variables
Variables Used
Radius 1 - Radius 1 is a radial line from the focus to any point of a curve. (Measured in Meter)
Number of cusps- Number of cusps is defined as the the number of curves made by the small circle of hypocycloid
STEP 1: Convert Input(s) to Base Unit
Radius 1: 11 Meter --> 11 Meter No Conversion Required
Number of cusps: 3 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
P = (8*r1*(n-1))/n --> (8*11*(3-1))/3
Evaluating ... ...
P = 58.6666666666667
STEP 3: Convert Result to Output's Unit
58.6666666666667 Meter --> No Conversion Required
FINAL ANSWER
58.6666666666667 Meter <-- Perimeter
(Calculation completed in 00.047 seconds)

11 Other formulas that you can solve using the same Inputs

Lateral Surface Area of a Conical Frustum
lateral_surface_area = pi*(Radius 1+Radius 2)*sqrt((Radius 1-Radius 2)^2+Height^2) Go
Volume of a Conical Frustum
volume = (1/3)*pi*Height*(Radius 1^2+Radius 2^2+(Radius 1*Radius 2)) Go
Moment of Inertia of a solid sphere about its diameter
moment_of_inertia = 2*(Mass*(Radius 1^2))/5 Go
Moment of inertia of a circular disc about an axis through its center and perpendicular to its plane
moment_of_inertia = (Mass*(Radius 1^2))/2 Go
Moment of Inertia of a right circular solid cylinder about its symmetry axis
moment_of_inertia = (Mass*(Radius 1^2))/2 Go
Moment of Inertia of a spherical shell about its diameter
moment_of_inertia = 2*(Mass*(Radius 1))/3 Go
Moment of Inertia of a right circular hollow cylinder about its axis
moment_of_inertia = (Mass*(Radius 1)^2) Go
Moment of inertia of a circular ring about an axis through its center and perpendicular to its plane
moment_of_inertia = Mass*(Radius 1^2) Go
Top Surface Area of a Conical Frustum
top_surface_area = pi*(Radius 1)^2 Go
Area of a Torus
area = pi^2*(Radius 2^2-Radius 1^2) Go
Volume of cylinder circumscribing a sphere when radius of sphere is known
volume = 2*pi*(Radius 1^3) Go

11 Other formulas that calculate the same Output

Perimeter of a Right Angled Triangle
perimeter = Side A+Side B+sqrt(Side A^2+Side B^2) Go
Perimeter of a rectangle when diagonal and length are given
perimeter = 2*(Length+sqrt((Diagonal)^2-(Length)^2)) Go
Perimeter Of Parallelepiped
perimeter = 4*Side A+4*Side B+4*Side C Go
Perimeter of a Parallelogram
perimeter = 2*Side A+2*Side B Go
Perimeter of a Kite
perimeter = 2*(Side A+Side B) Go
Perimeter of a rectangle when length and width are given
perimeter = 2*Length+2*Width Go
Perimeter of an Isosceles Triangle
perimeter = Side A+2*Side B Go
Perimeter of a Cube
perimeter = 12*Side Go
Perimeter of a square when side is given
perimeter = 4*Side Go
Perimeter of an Equilateral Triangle
perimeter = 3*Side Go
Perimeter of a Rhombus
perimeter = 4*Side Go

Perimeter of hypocycloid Formula

perimeter = (8*Radius 1*(Number of cusps-1))/Number of cusps
P = (8*r1*(n-1))/n

What is a hypocycloid?

In geometry, a hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. As the radius of the larger circle is increased, the hypocycloid becomes more like the cycloid created by rolling a circle on a line. Any hypocycloid with an integral value of k, and thus k cusps, can move snugly inside another hypocycloid with k+1 cusps, such that the points of the smaller hypocycloid will always be in contact with the larger. This motion looks like 'rolling', though it is not technically rolling in the sense of classical mechanics, since it involves slipping.

How to Calculate Perimeter of hypocycloid?

Perimeter of hypocycloid calculator uses perimeter = (8*Radius 1*(Number of cusps-1))/Number of cusps to calculate the Perimeter, The Perimeter of hypocycloid formula is defined as the outermost parts or boundary of a hypocycloid, where p = perimeter of hypocycloid, radius_1 = radius of hypocycloid. Perimeter and is denoted by P symbol.

How to calculate Perimeter of hypocycloid using this online calculator? To use this online calculator for Perimeter of hypocycloid, enter Radius 1 (r1) and Number of cusps (n) and hit the calculate button. Here is how the Perimeter of hypocycloid calculation can be explained with given input values -> 58.66667 = (8*11*(3-1))/3.

FAQ

What is Perimeter of hypocycloid?
The Perimeter of hypocycloid formula is defined as the outermost parts or boundary of a hypocycloid, where p = perimeter of hypocycloid, radius_1 = radius of hypocycloid and is represented as P = (8*r1*(n-1))/n or perimeter = (8*Radius 1*(Number of cusps-1))/Number of cusps. Radius 1 is a radial line from the focus to any point of a curve and Number of cusps is defined as the the number of curves made by the small circle of hypocycloid.
How to calculate Perimeter of hypocycloid?
The Perimeter of hypocycloid formula is defined as the outermost parts or boundary of a hypocycloid, where p = perimeter of hypocycloid, radius_1 = radius of hypocycloid is calculated using perimeter = (8*Radius 1*(Number of cusps-1))/Number of cusps. To calculate Perimeter of hypocycloid, you need Radius 1 (r1) and Number of cusps (n). With our tool, you need to enter the respective value for Radius 1 and Number of cusps 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 Perimeter?
In this formula, Perimeter uses Radius 1 and Number of cusps. We can use 11 other way(s) to calculate the same, which is/are as follows -
  • perimeter = 2*Length+2*Width
  • perimeter = 4*Side
  • perimeter = 3*Side
  • perimeter = 2*Side A+2*Side B
  • perimeter = 4*Side
  • perimeter = Side A+2*Side B
  • perimeter = Side A+Side B+sqrt(Side A^2+Side B^2)
  • perimeter = 12*Side
  • perimeter = 2*(Side A+Side B)
  • perimeter = 4*Side A+4*Side B+4*Side C
  • perimeter = 2*(Length+sqrt((Diagonal)^2-(Length)^2))
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