Area of Hypocycloid Solution

STEP 0: Pre-Calculation Summary
Formula Used
Area of Hypocycloid = pi*((Number of Cusps of Hypocycloid-1)*(Number of Cusps of Hypocycloid-2))/(Number of Cusps of Hypocycloid^2)*Larger Radius of Hypocycloid^2
A = pi*((NCusps-1)*(NCusps-2))/(NCusps^2)*rLarge^2
This formula uses 1 Constants, 3 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
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.
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.
STEP 1: Convert Input(s) to Base Unit
Number of Cusps of Hypocycloid: 5 --> No Conversion Required
Larger Radius of Hypocycloid: 10 Meter --> 10 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
A = pi*((NCusps-1)*(NCusps-2))/(NCusps^2)*rLarge^2 --> pi*((5-1)*(5-2))/(5^2)*10^2
Evaluating ... ...
A = 150.79644737231
STEP 3: Convert Result to Output's Unit
150.79644737231 Square Meter --> No Conversion Required
FINAL ANSWER
150.79644737231 150.7964 Square Meter <-- Area of Hypocycloid
(Calculation completed in 00.008 seconds)

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Indian Institute of Information Technology (IIIT), Bhopal
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Area and Number of Cusps of Hypocycloid Calculators

Area of Hypocycloid given Chord Length
​ LaTeX ​ Go Area of Hypocycloid = pi*((Number of Cusps of Hypocycloid-1)*(Number of Cusps of Hypocycloid-2))/(Number of Cusps of Hypocycloid^2)*(Chord Length of Hypocycloid/(2*sin(pi/Number of Cusps of Hypocycloid)))^2
Area of Hypocycloid
​ LaTeX ​ Go Area of Hypocycloid = pi*((Number of Cusps of Hypocycloid-1)*(Number of Cusps of Hypocycloid-2))/(Number of Cusps of Hypocycloid^2)*Larger Radius of Hypocycloid^2
Area of Hypocycloid given Perimeter
​ LaTeX ​ Go Area of Hypocycloid = pi/64*(Number of Cusps of Hypocycloid-2)/(Number of Cusps of Hypocycloid-1)*Perimeter of Hypocycloid^2
Number of Cusps of Hypocycloid
​ LaTeX ​ Go Number of Cusps of Hypocycloid = Larger Radius of Hypocycloid/Smaller Radius of Hypocycloid

Area of Hypocycloid Formula

​LaTeX ​Go
Area of Hypocycloid = pi*((Number of Cusps of Hypocycloid-1)*(Number of Cusps of Hypocycloid-2))/(Number of Cusps of Hypocycloid^2)*Larger Radius of Hypocycloid^2
A = pi*((NCusps-1)*(NCusps-2))/(NCusps^2)*rLarge^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 Area of Hypocycloid?

Area of Hypocycloid calculator uses Area of Hypocycloid = pi*((Number of Cusps of Hypocycloid-1)*(Number of Cusps of Hypocycloid-2))/(Number of Cusps of Hypocycloid^2)*Larger Radius of Hypocycloid^2 to calculate the Area of Hypocycloid, Area of Hypocycloid formula is defined as the total quantity of plane enclosed by the boundary of the Hypocycloid. Area of Hypocycloid is denoted by A symbol.

How to calculate Area of Hypocycloid using this online calculator? To use this online calculator for Area of Hypocycloid, enter Number of Cusps of Hypocycloid (NCusps) & Larger Radius of Hypocycloid (rLarge) and hit the calculate button. Here is how the Area of Hypocycloid calculation can be explained with given input values -> 150.7964 = pi*((5-1)*(5-2))/(5^2)*10^2.

FAQ

What is Area of Hypocycloid?
Area of Hypocycloid formula is defined as the total quantity of plane enclosed by the boundary of the Hypocycloid and is represented as A = pi*((NCusps-1)*(NCusps-2))/(NCusps^2)*rLarge^2 or Area of Hypocycloid = pi*((Number of Cusps of Hypocycloid-1)*(Number of Cusps of Hypocycloid-2))/(Number of Cusps of Hypocycloid^2)*Larger Radius of Hypocycloid^2. Number of Cusps of Hypocycloid is the number of sharp tips or the round edged spikes of the Hypocycloid & Larger Radius of Hypocycloid is the radius of the larger circle of Hypocycloid or the circle inside which the Hypocycloid shape is inscribed.
How to calculate Area of Hypocycloid?
Area of Hypocycloid formula is defined as the total quantity of plane enclosed by the boundary of the Hypocycloid is calculated using Area of Hypocycloid = pi*((Number of Cusps of Hypocycloid-1)*(Number of Cusps of Hypocycloid-2))/(Number of Cusps of Hypocycloid^2)*Larger Radius of Hypocycloid^2. To calculate Area of Hypocycloid, you need Number of Cusps of Hypocycloid (NCusps) & Larger Radius of Hypocycloid (rLarge). With our tool, you need to enter the respective value for Number of Cusps of Hypocycloid & Larger Radius 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 Area of Hypocycloid?
In this formula, Area of Hypocycloid uses Number of Cusps of Hypocycloid & Larger Radius of Hypocycloid. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Area of Hypocycloid = pi*((Number of Cusps of Hypocycloid-1)*(Number of Cusps of Hypocycloid-2))/(Number of Cusps of Hypocycloid^2)*(Chord Length of Hypocycloid/(2*sin(pi/Number of Cusps of Hypocycloid)))^2
  • Area of Hypocycloid = pi/64*(Number of Cusps of Hypocycloid-2)/(Number of Cusps of Hypocycloid-1)*Perimeter of Hypocycloid^2
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