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Area of Section of Lune Calculator

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✖The Radius of Smaller Circle of Lune is the radius of the circle with lesser size, out of the two circles using which the Lune is created.ⓘ Radius of Smaller Circle of Lune [r_Smaller]			+10% -10%
✖The Area of Triangle of Lune is the total quantity of plane occupied by the triangle joining the centers of two circles of Lune and one of their intersecting point.ⓘ Area of Triangle of Lune [A_Triangle]			+10% -10%
✖The Radius of Larger Circle of Lune is the radius of the circle with greater size, out of the two circles using which the Lune is created.ⓘ Radius of Larger Circle of Lune [r_Larger]			+10% -10%
✖The Distance of Centers of Circles of Lune is the length of the line joining the centers of two circles with which the Lune is created.ⓘ Distance of Centers of Circles of Lune [d_Centers]			+10% -10%

✖The Area of Section of Lune is the total quantity of plane occupied by the section formed between the larger and smaller Lunes in the Lune shape or the portion of intersection of circles in the Lune.ⓘ Area of Section of Lune [A_Section]

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Area of Section of Lune Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Section of Lune = (pi*Radius of Smaller Circle of Lune^2)-((2*Area of Triangle of Lune)+(Radius of Smaller Circle of Lune^2*arccos((Radius of Larger Circle of Lune^2-Radius of Smaller Circle of Lune^2-Distance of Centers of Circles of Lune^2)/(2*Radius of Smaller Circle of Lune*Distance of Centers of Circles of Lune)))-(Radius of Larger Circle of Lune^2*arccos((Radius of Larger Circle of Lune^2+Distance of Centers of Circles of Lune^2-Radius of Smaller Circle of Lune^2)/(2*Radius of Larger Circle of Lune*Distance of Centers of Circles of Lune))))
A_Section = (pi*r_Smaller^2)-((2*A_Triangle)+(r_Smaller^2*arccos((r_Larger^2-r_Smaller^2-d_Centers^2)/(2*r_Smaller*d_Centers)))-(r_Larger^2*arccos((r_Larger^2+d_Centers^2-r_Smaller^2)/(2*r_Larger*d_Centers))))
This formula uses 1 Constants, 2 Functions, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
arccos - Arccosine function, is the inverse function of the cosine function.It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., arccos(Number)

Variables Used

Area of Section of Lune - (Measured in Square Meter) - The Area of Section of Lune is the total quantity of plane occupied by the section formed between the larger and smaller Lunes in the Lune shape or the portion of intersection of circles in the Lune.
Radius of Smaller Circle of Lune - (Measured in Meter) - The Radius of Smaller Circle of Lune is the radius of the circle with lesser size, out of the two circles using which the Lune is created.
Area of Triangle of Lune - (Measured in Square Meter) - The Area of Triangle of Lune is the total quantity of plane occupied by the triangle joining the centers of two circles of Lune and one of their intersecting point.
Radius of Larger Circle of Lune - (Measured in Meter) - The Radius of Larger Circle of Lune is the radius of the circle with greater size, out of the two circles using which the Lune is created.
Distance of Centers of Circles of Lune - (Measured in Meter) - The Distance of Centers of Circles of Lune is the length of the line joining the centers of two circles with which the Lune is created.

STEP 1: Convert Input(s) to Base Unit

Radius of Smaller Circle of Lune: 5 Meter --> 5 Meter No Conversion Required
Area of Triangle of Lune: 20 Square Meter --> 20 Square Meter No Conversion Required
Radius of Larger Circle of Lune: 8 Meter --> 8 Meter No Conversion Required
Distance of Centers of Circles of Lune: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A_Section = (pi*r_Smaller^2)-((2*A_Triangle)+(r_Smaller^2*arccos((r_Larger^2-r_Smaller^2-d_Centers^2)/(2*r_Smaller*d_Centers)))-(r_Larger^2*arccos((r_Larger^2+d_Centers^2-r_Smaller^2)/(2*r_Larger*d_Centers)))) --> (pi*5^2)-((2*20)+(5^2*arccos((8^2-5^2-10^2)/(2*5*10)))-(8^2*arccos((8^2+10^2-5^2)/(2*8*10))))

Evaluating ... ...

A_Section = 16.0283034451678

STEP 3: Convert Result to Output's Unit

16.0283034451678 Square Meter --> No Conversion Required

FINAL ANSWER

16.0283034451678 ≈ 16.0283 Square Meter <-- Area of Section of Lune

(Calculation completed in 00.004 seconds)

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Created by Jaseem K

IIT Madras (IIT Madras), Chennai

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The National Institute of Engineering (NIE), Mysuru

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< Lune Calculators

Area of Large Lune

LaTeX Go Area of Large Lune = (pi*(Radius of Larger Circle of Lune^2-Radius of Smaller Circle of Lune^2))+(2*Area of Triangle of Lune)+(Radius of Smaller Circle of Lune^2*arccos((Radius of Larger Circle of Lune^2-Radius of Smaller Circle of Lune^2-Distance of Centers of Circles of Lune^2)/(2*Radius of Smaller Circle of Lune*Distance of Centers of Circles of Lune)))-(Radius of Larger Circle of Lune^2*arccos((Radius of Larger Circle of Lune^2+Distance of Centers of Circles of Lune^2-Radius of Smaller Circle of Lune^2)/(2*Radius of Larger Circle of Lune*Distance of Centers of Circles of Lune)))

Area of Section of Lune

LaTeX Go Area of Section of Lune = (pi*Radius of Smaller Circle of Lune^2)-((2*Area of Triangle of Lune)+(Radius of Smaller Circle of Lune^2*arccos((Radius of Larger Circle of Lune^2-Radius of Smaller Circle of Lune^2-Distance of Centers of Circles of Lune^2)/(2*Radius of Smaller Circle of Lune*Distance of Centers of Circles of Lune)))-(Radius of Larger Circle of Lune^2*arccos((Radius of Larger Circle of Lune^2+Distance of Centers of Circles of Lune^2-Radius of Smaller Circle of Lune^2)/(2*Radius of Larger Circle of Lune*Distance of Centers of Circles of Lune))))

Area of Small Lune

LaTeX Go Area of Small Lune = (2*Area of Triangle of Lune)+(Radius of Smaller Circle of Lune^2*arccos((Radius of Larger Circle of Lune^2-Radius of Smaller Circle of Lune^2-Distance of Centers of Circles of Lune^2)/(2*Radius of Smaller Circle of Lune*Distance of Centers of Circles of Lune)))-(Radius of Larger Circle of Lune^2*arccos((Radius of Larger Circle of Lune^2+Distance of Centers of Circles of Lune^2-Radius of Smaller Circle of Lune^2)/(2*Radius of Larger Circle of Lune*Distance of Centers of Circles of Lune)))

Area of Triangle of Lune

LaTeX Go Area of Triangle of Lune = sqrt((Radius of Smaller Circle of Lune+Radius of Larger Circle of Lune+Distance of Centers of Circles of Lune)*(Radius of Larger Circle of Lune+Distance of Centers of Circles of Lune-Radius of Smaller Circle of Lune)*(Distance of Centers of Circles of Lune+Radius of Smaller Circle of Lune-Radius of Larger Circle of Lune)*(Radius of Smaller Circle of Lune+Radius of Larger Circle of Lune-Distance of Centers of Circles of Lune))/4

Area of Section of Lune Formula

LaTeX Go

What is a Lune?

When two circle intersects each other, and remove the intersection part. The shape thus obtained is called a Lune. The Latin word 'luna' means 'moon'. The shape Lune is actually a combination of two crescent moon shapes joined each other and facing oppositely.

How to Calculate Area of Section of Lune?

Area of Section of Lune calculator uses Area of Section of Lune = (pi*Radius of Smaller Circle of Lune^2)-((2*Area of Triangle of Lune)+(Radius of Smaller Circle of Lune^2*arccos((Radius of Larger Circle of Lune^2-Radius of Smaller Circle of Lune^2-Distance of Centers of Circles of Lune^2)/(2*Radius of Smaller Circle of Lune*Distance of Centers of Circles of Lune)))-(Radius of Larger Circle of Lune^2*arccos((Radius of Larger Circle of Lune^2+Distance of Centers of Circles of Lune^2-Radius of Smaller Circle of Lune^2)/(2*Radius of Larger Circle of Lune*Distance of Centers of Circles of Lune)))) to calculate the Area of Section of Lune, The Area of Section of Lune formula is defined as the total quantity of plane bounded by the portion of intersection in the Lune shape. Area of Section of Lune is denoted by A_Section symbol.

How to calculate Area of Section of Lune using this online calculator? To use this online calculator for Area of Section of Lune, enter Radius of Smaller Circle of Lune (r_Smaller), Area of Triangle of Lune (A_Triangle), Radius of Larger Circle of Lune (r_Larger) & Distance of Centers of Circles of Lune (d_Centers) and hit the calculate button. Here is how the Area of Section of Lune calculation can be explained with given input values -> 16.0283 = (pi*5^2)-((2*20)+(5^2*arccos((8^2-5^2-10^2)/(2*5*10)))-(8^2*arccos((8^2+10^2-5^2)/(2*8*10)))).

FAQ

What is Area of Section of Lune?

The Area of Section of Lune formula is defined as the total quantity of plane bounded by the portion of intersection in the Lune shape and is represented as A_Section = (pi*r_Smaller^2)-((2*A_Triangle)+(r_Smaller^2*arccos((r_Larger^2-r_Smaller^2-d_Centers^2)/(2*r_Smaller*d_Centers)))-(r_Larger^2*arccos((r_Larger^2+d_Centers^2-r_Smaller^2)/(2*r_Larger*d_Centers)))) or Area of Section of Lune = (pi*Radius of Smaller Circle of Lune^2)-((2*Area of Triangle of Lune)+(Radius of Smaller Circle of Lune^2*arccos((Radius of Larger Circle of Lune^2-Radius of Smaller Circle of Lune^2-Distance of Centers of Circles of Lune^2)/(2*Radius of Smaller Circle of Lune*Distance of Centers of Circles of Lune)))-(Radius of Larger Circle of Lune^2*arccos((Radius of Larger Circle of Lune^2+Distance of Centers of Circles of Lune^2-Radius of Smaller Circle of Lune^2)/(2*Radius of Larger Circle of Lune*Distance of Centers of Circles of Lune)))). The Radius of Smaller Circle of Lune is the radius of the circle with lesser size, out of the two circles using which the Lune is created, The Area of Triangle of Lune is the total quantity of plane occupied by the triangle joining the centers of two circles of Lune and one of their intersecting point, The Radius of Larger Circle of Lune is the radius of the circle with greater size, out of the two circles using which the Lune is created & The Distance of Centers of Circles of Lune is the length of the line joining the centers of two circles with which the Lune is created.

How to calculate Area of Section of Lune?

The Area of Section of Lune formula is defined as the total quantity of plane bounded by the portion of intersection in the Lune shape is calculated using Area of Section of Lune = (pi*Radius of Smaller Circle of Lune^2)-((2*Area of Triangle of Lune)+(Radius of Smaller Circle of Lune^2*arccos((Radius of Larger Circle of Lune^2-Radius of Smaller Circle of Lune^2-Distance of Centers of Circles of Lune^2)/(2*Radius of Smaller Circle of Lune*Distance of Centers of Circles of Lune)))-(Radius of Larger Circle of Lune^2*arccos((Radius of Larger Circle of Lune^2+Distance of Centers of Circles of Lune^2-Radius of Smaller Circle of Lune^2)/(2*Radius of Larger Circle of Lune*Distance of Centers of Circles of Lune)))). To calculate Area of Section of Lune, you need Radius of Smaller Circle of Lune (r_Smaller), Area of Triangle of Lune (A_Triangle), Radius of Larger Circle of Lune (r_Larger) & Distance of Centers of Circles of Lune (d_Centers). With our tool, you need to enter the respective value for Radius of Smaller Circle of Lune, Area of Triangle of Lune, Radius of Larger Circle of Lune & Distance of Centers of Circles of Lune and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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