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Area of Small Lune Calculator

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✖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 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 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 Small Lune is the total quantity of plane occupied by the smaller lune portion in the Lune shape.ⓘ Area of Small Lune [A_Small]

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Area of Small Lune Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
A_Small = (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 2 Functions, 5 Variables

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 Small Lune - (Measured in Square Meter) - The Area of Small Lune is the total quantity of plane occupied by the smaller lune portion in the Lune shape.
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 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.
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

Area of Triangle of Lune: 20 Square Meter --> 20 Square Meter No Conversion Required
Radius of Smaller Circle of Lune: 5 Meter --> 5 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_Small = (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))) --> (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_Small = 62.5115128945771

STEP 3: Convert Result to Output's Unit

62.5115128945771 Square Meter --> No Conversion Required

FINAL ANSWER

62.5115128945771 ≈ 62.51151 Square Meter <-- Area of Small 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 Small 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 Small Lune?

Area of Small Lune calculator uses 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))) to calculate the Area of Small Lune, The Area of Small Lune formula is defined as total quantity of plane occupied by the smaller Lune portion of the Lune shape. Area of Small Lune is denoted by A_Small symbol.

How to calculate Area of Small Lune using this online calculator? To use this online calculator for Area of Small Lune, enter Area of Triangle of Lune (A_Triangle), Radius of Smaller Circle of Lune (r_Smaller), 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 Small Lune calculation can be explained with given input values -> 62.51151 = (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 Small Lune?

The Area of Small Lune formula is defined as total quantity of plane occupied by the smaller Lune portion of the Lune shape and is represented as A_Small = (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 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))). 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 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 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 Small Lune?

The Area of Small Lune formula is defined as total quantity of plane occupied by the smaller Lune portion of the Lune shape is calculated using 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))). To calculate Area of Small Lune, you need Area of Triangle of Lune (A_Triangle), Radius of Smaller Circle of Lune (r_Smaller), 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 Area of Triangle of Lune, Radius of Smaller Circle 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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