Larger Radius of Hypocycloid given Area Calculator

✖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%
✖Area of Hypocycloid is the total quantity of plane enclosed by the boundary of the Hypocycloid.ⓘ Area of Hypocycloid [A]			+10% -10%

✖Larger Radius of Hypocycloid is the radius of the larger circle of Hypocycloid or the circle inside which the Hypocycloid shape is inscribed.ⓘ Larger Radius of Hypocycloid given Area [r_Large]

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Larger Radius of Hypocycloid given Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Larger Radius of Hypocycloid = Number of Cusps of Hypocycloid*sqrt(Area of Hypocycloid/(pi*(Number of Cusps of Hypocycloid-1)*(Number of Cusps of Hypocycloid-2)))
r_Large = N_Cusps*sqrt(A/(pi*(N_Cusps-1)*(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

Larger Radius of Hypocycloid - (Measured in Meter) - Larger Radius of Hypocycloid is the radius of the larger circle of Hypocycloid or the circle inside which the Hypocycloid shape is inscribed.
Number of Cusps of Hypocycloid - Number of Cusps of Hypocycloid is the number of sharp tips or the round edged spikes 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.

STEP 1: Convert Input(s) to Base Unit

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

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

Evaluating ... ...

r_Large = 9.97355701003582

STEP 3: Convert Result to Output's Unit

9.97355701003582 Meter --> No Conversion Required

FINAL ANSWER

9.97355701003582 ≈ 9.973557 Meter <-- Larger Radius of Hypocycloid

(Calculation completed in 00.007 seconds)

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< Radius of Large Circle of Hypocycloid Calculators

Larger Radius of Hypocycloid given Area

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

Larger Radius of Hypocycloid given Chord Length

LaTeX Go Larger Radius of Hypocycloid = Chord Length of Hypocycloid/(2*sin(pi/Number of Cusps of Hypocycloid))

Larger Radius of Hypocycloid given Perimeter

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

Larger Radius of Hypocycloid given Smaller Radius

LaTeX Go Larger Radius of Hypocycloid = Number of Cusps of Hypocycloid*Smaller Radius of Hypocycloid

Larger Radius of Hypocycloid given Area Formula

LaTeX Go

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 Larger Radius of Hypocycloid given Area?

Larger Radius of Hypocycloid given Area calculator uses Larger Radius of Hypocycloid = Number of Cusps of Hypocycloid*sqrt(Area of Hypocycloid/(pi*(Number of Cusps of Hypocycloid-1)*(Number of Cusps of Hypocycloid-2))) to calculate the Larger Radius of Hypocycloid, Larger Radius of Hypocycloid given Area is defined as the radius of the larger circle of Hypocycloid or the circle inside which the Hypocycloid shape is inscribed, and calculated using the area of the Hypocycloid. Larger Radius of Hypocycloid is denoted by r_Large symbol.

How to calculate Larger Radius of Hypocycloid given Area using this online calculator? To use this online calculator for Larger Radius of Hypocycloid given Area, enter Number of Cusps of Hypocycloid (N_Cusps) & Area of Hypocycloid (A) and hit the calculate button. Here is how the Larger Radius of Hypocycloid given Area calculation can be explained with given input values -> 9.973557 = 5*sqrt(150/(pi*(5-1)*(5-2))).

FAQ

What is Larger Radius of Hypocycloid given Area?

Larger Radius of Hypocycloid given Area is defined as the radius of the larger circle of Hypocycloid or the circle inside which the Hypocycloid shape is inscribed, and calculated using the area of the Hypocycloid and is represented as r_Large = N_Cusps*sqrt(A/(pi*(N_Cusps-1)*(N_Cusps-2))) or Larger Radius of Hypocycloid = Number of Cusps of Hypocycloid*sqrt(Area of Hypocycloid/(pi*(Number of Cusps of Hypocycloid-1)*(Number of Cusps of Hypocycloid-2))). Number of Cusps of Hypocycloid is the number of sharp tips or the round edged spikes of the Hypocycloid & Area of Hypocycloid is the total quantity of plane enclosed by the boundary of the Hypocycloid.

How to calculate Larger Radius of Hypocycloid given Area?

Larger Radius of Hypocycloid given Area is defined as the radius of the larger circle of Hypocycloid or the circle inside which the Hypocycloid shape is inscribed, and calculated using the area of the Hypocycloid is calculated using Larger Radius of Hypocycloid = Number of Cusps of Hypocycloid*sqrt(Area of Hypocycloid/(pi*(Number of Cusps of Hypocycloid-1)*(Number of Cusps of Hypocycloid-2))). To calculate Larger Radius of Hypocycloid given Area, you need Number of Cusps of Hypocycloid (N_Cusps) & Area of Hypocycloid (A). With our tool, you need to enter the respective value for Number of Cusps of Hypocycloid & Area 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 Larger Radius of Hypocycloid?

In this formula, Larger Radius of Hypocycloid uses Number of Cusps of Hypocycloid & Area of Hypocycloid. We can use 3 other way(s) to calculate the same, which is/are as follows -

Larger Radius of Hypocycloid = Number of Cusps of Hypocycloid*Smaller Radius of Hypocycloid
Larger Radius of Hypocycloid = Chord Length of Hypocycloid/(2*sin(pi/Number of Cusps of Hypocycloid))
Larger Radius of Hypocycloid = (Perimeter of Hypocycloid*Number of Cusps of Hypocycloid)/(8*(Number of Cusps of Hypocycloid-1))

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