Perimeter of Hypocycloid given Area Calculator

✖Area of Hypocycloid is the total quantity of plane enclosed by the boundary of the Hypocycloid.ⓘ Area of Hypocycloid [A]			+10% -10%
✖Number of Cusps of Hypocycloid is the number of sharp tips or the round edged spikes of the Hypocycloid.ⓘ Number of Cusps of Hypocycloid [N_Cusps]			+10% -10%

✖Perimeter of Hypocycloid is the total length of all the boundary edges of the Hypocycloid.ⓘ Perimeter of Hypocycloid given Area [P]

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Perimeter of Hypocycloid given Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Perimeter of Hypocycloid = 8*sqrt((Area of Hypocycloid*(Number of Cusps of Hypocycloid-1))/(pi*(Number of Cusps of Hypocycloid-2)))
P = 8*sqrt((A*(N_Cusps-1))/(pi*(N_Cusps-2)))
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Perimeter of Hypocycloid - (Measured in Meter) - Perimeter of Hypocycloid is the total length of all the boundary edges of the Hypocycloid.
Area of Hypocycloid - (Measured in Square Meter) - Area of Hypocycloid is the total quantity of plane enclosed by the boundary of the Hypocycloid.
Number of Cusps of Hypocycloid - Number of Cusps of Hypocycloid is the number of sharp tips or the round edged spikes of the Hypocycloid.

STEP 1: Convert Input(s) to Base Unit

Area of Hypocycloid: 150 Square Meter --> 150 Square Meter No Conversion Required
Number of Cusps of Hypocycloid: 5 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P = 8*sqrt((A*(N_Cusps-1))/(pi*(N_Cusps-2))) --> 8*sqrt((150*(5-1))/(pi*(5-2)))

Evaluating ... ...

P = 63.8307648642292

STEP 3: Convert Result to Output's Unit

63.8307648642292 Meter --> No Conversion Required

FINAL ANSWER

63.8307648642292 ≈ 63.83076 Meter <-- Perimeter of Hypocycloid

(Calculation completed in 00.004 seconds)

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< Perimeter of Hypocycloid Calculators

Perimeter of Hypocycloid given Chord Length

LaTeX Go Perimeter of Hypocycloid = (4*Chord Length of Hypocycloid)/(sin(pi/Number of Cusps of Hypocycloid))*(Number of Cusps of Hypocycloid-1)/Number of Cusps of Hypocycloid

Perimeter of Hypocycloid given Area

LaTeX Go Perimeter of Hypocycloid = 8*sqrt((Area of Hypocycloid*(Number of Cusps of Hypocycloid-1))/(pi*(Number of Cusps of Hypocycloid-2)))

Perimeter of Hypocycloid

LaTeX Go Perimeter of Hypocycloid = (8*Larger Radius of Hypocycloid*(Number of Cusps of Hypocycloid-1))/Number of Cusps of Hypocycloid

Perimeter of Hypocycloid given Area Formula

LaTeX Go

Perimeter of Hypocycloid = 8*sqrt((Area of Hypocycloid*(Number of Cusps of Hypocycloid-1))/(pi*(Number of Cusps of Hypocycloid-2)))
P = 8*sqrt((A*(N_Cusps-1))/(pi*(N_Cusps-2)))

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 given Area?

Perimeter of Hypocycloid given Area calculator uses Perimeter of Hypocycloid = 8*sqrt((Area of Hypocycloid*(Number of Cusps of Hypocycloid-1))/(pi*(Number of Cusps of Hypocycloid-2))) to calculate the Perimeter of Hypocycloid, Perimeter of Hypocycloid given Area is defined as the total length of all the boundary edges of the Hypocycloid, and calculated using the area of the Hypocycloid. Perimeter of Hypocycloid is denoted by P symbol.

How to calculate Perimeter of Hypocycloid given Area using this online calculator? To use this online calculator for Perimeter of Hypocycloid given Area, enter Area of Hypocycloid (A) & Number of Cusps of Hypocycloid (N_Cusps) and hit the calculate button. Here is how the Perimeter of Hypocycloid given Area calculation can be explained with given input values -> 63.83076 = 8*sqrt((150*(5-1))/(pi*(5-2))).

FAQ

What is Perimeter of Hypocycloid given Area?

Perimeter of Hypocycloid given Area is defined as the total length of all the boundary edges of the Hypocycloid, and calculated using the area of the Hypocycloid and is represented as P = 8*sqrt((A*(N_Cusps-1))/(pi*(N_Cusps-2))) or Perimeter of Hypocycloid = 8*sqrt((Area of Hypocycloid*(Number of Cusps of Hypocycloid-1))/(pi*(Number of Cusps of Hypocycloid-2))). Area of Hypocycloid is the total quantity of plane enclosed by the boundary of the Hypocycloid & Number of Cusps of Hypocycloid is the number of sharp tips or the round edged spikes of the Hypocycloid.

How to calculate Perimeter of Hypocycloid given Area?

Perimeter of Hypocycloid given Area is defined as the total length of all the boundary edges of the Hypocycloid, and calculated using the area of the Hypocycloid is calculated using Perimeter of Hypocycloid = 8*sqrt((Area of Hypocycloid*(Number of Cusps of Hypocycloid-1))/(pi*(Number of Cusps of Hypocycloid-2))). To calculate Perimeter of Hypocycloid given Area, you need Area of Hypocycloid (A) & Number of Cusps of Hypocycloid (N_Cusps). With our tool, you need to enter the respective value for Area of Hypocycloid & Number of Cusps of Hypocycloid 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 of Hypocycloid?

In this formula, Perimeter of Hypocycloid uses Area of Hypocycloid & Number of Cusps of Hypocycloid. We can use 2 other way(s) to calculate the same, which is/are as follows -

Perimeter of Hypocycloid = (8*Larger Radius of Hypocycloid*(Number of Cusps of Hypocycloid-1))/Number of Cusps of Hypocycloid
Perimeter of Hypocycloid = (4*Chord Length of Hypocycloid)/(sin(pi/Number of Cusps of Hypocycloid))*(Number of Cusps of Hypocycloid-1)/Number of Cusps of Hypocycloid

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