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Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes Formula

GoArea of Elliptical Ring given Linear Eccentricities and Semi Minor Axes Formula

GoArea of Elliptical Ring given Width and Outer Semi Axes Formula

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Area of Elliptical Ring is the total quantity of plane enclosed between the outer and inner elliptical boundary edges of the Elliptical Ring. Check FAQs

A Ring = π \cdot ((\sqrt{{a Outer}^{2} - {c Outer}^{2}} \cdot a Outer) - (\sqrt{{a Inner}^{2} - {c Inner}^{2}} \cdot a Inner))

A_Ring - Area of Elliptical Ring?a_Outer - Outer Semi Major Axis of Elliptical Ring?c_Outer - Outer Linear Eccentricity of Elliptical Ring?a_Inner - Inner Semi Major Axis of Elliptical Ring?c_Inner - Inner Linear Eccentricity of Elliptical Ring?π - Archimedes' constant?

Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes Example

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Here is how the Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes equation looks like with Values.

Here is how the Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes equation looks like with Units.

Here is how the Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes equation looks like.

124.9979 = 3.1416 \cdot ((\sqrt{10^{2} - 6^{2}} \cdot 10) - (\sqrt{7^{2} - 4^{2}} \cdot 7))

124.9979m² = 3.1416 \cdot ((\sqrt{{10m}^{2} - {6m}^{2}} \cdot 10m) - (\sqrt{{7m}^{2} - {4m}^{2}} \cdot 7m))

124.9979 = 3.1416 \cdot ((\sqrt{10^{2} - 6^{2}} \cdot 10) - (\sqrt{7^{2} - 4^{2}} \cdot 7))

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Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes Solution

Follow our step by step solution on how to calculate Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes?

FIRST Step Consider the formula

A Ring = π \cdot ((\sqrt{{a Outer}^{2} - {c Outer}^{2}} \cdot a Outer) - (\sqrt{{a Inner}^{2} - {c Inner}^{2}} \cdot a Inner))

Next Step Substitute values of Variables

∴

A Ring = π \cdot ((\sqrt{{10m}^{2} - {6m}^{2}} \cdot 10m) - (\sqrt{{7m}^{2} - {4m}^{2}} \cdot 7m))

Next Step Substitute values of Constants

∴

A Ring = 3.1416 \cdot ((\sqrt{{10m}^{2} - {6m}^{2}} \cdot 10m) - (\sqrt{{7m}^{2} - {4m}^{2}} \cdot 7m))

Next Step Prepare to Evaluate

∴

A Ring = 3.1416 \cdot ((\sqrt{10^{2} - 6^{2}} \cdot 10) - (\sqrt{7^{2} - 4^{2}} \cdot 7))

Next Step Evaluate

∴

A Ring = 124.997881628032m²

LAST Step Rounding Answer

∴

A Ring = 124.9979m²

Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes Formula Elements

Variables

Constants

Functions

Area of Elliptical Ring

Area of Elliptical Ring is the total quantity of plane enclosed between the outer and inner elliptical boundary edges of the Elliptical Ring.

Symbol: A_Ring

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area of Elliptical Ring

Outer Semi Major Axis of Elliptical Ring

Outer Semi Major Axis of Elliptical Ring is half of the length of the chord of the outer ellipse which passing through both foci of the outer ellipse of the Elliptical Ring.

Symbol: a_Outer

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Outer Semi Major Axis of Elliptical Ring

Outer Linear Eccentricity of Elliptical Ring

Outer Linear Eccentricity of Elliptical Ring is the distance from center of the Elliptical Ring to any of the foci of the outer ellipse.

Symbol: c_Outer

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Outer Linear Eccentricity of Elliptical Ring

Inner Semi Major Axis of Elliptical Ring

Inner Semi Major Axis of Elliptical Ring is half of the length of the chord of the inner ellipse which passing through both foci of the inner ellipse of the Elliptical Ring.

Symbol: a_Inner

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inner Semi Major Axis of Elliptical Ring

Inner Linear Eccentricity of Elliptical Ring

Inner Linear Eccentricity of Elliptical Ring is the distance from center of the Elliptical Ring to any of the foci of the inner ellipse.

Symbol: c_Inner

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inner Linear Eccentricity of Elliptical Ring

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sqrt(Number)

Other Formulas to find Area of Elliptical Ring

Go Area of Elliptical Ring given Linear Eccentricities and Semi Minor Axes

A Ring = π \cdot ((\sqrt{{b Outer}^{2} + {c Outer}^{2}} \cdot b Outer) - (\sqrt{{b Inner}^{2} + {c Inner}^{2}} \cdot b Inner))

Go Area of Elliptical Ring given Width and Outer Semi Axes

A Ring = π \cdot ((a Outer \cdot b Outer) - ((a Outer - w Ring) \cdot (b Outer - w Ring)))

Go Area of Elliptical Ring

A Ring = π \cdot ((a Outer \cdot b Outer) - (a Inner \cdot b Inner))

How to Evaluate Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes?

Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes evaluator uses Area of Elliptical Ring = pi*((sqrt(Outer Semi Major Axis of Elliptical Ring^2-Outer Linear Eccentricity of Elliptical Ring^2)*Outer Semi Major Axis of Elliptical Ring)-(sqrt(Inner Semi Major Axis of Elliptical Ring^2-Inner Linear Eccentricity of Elliptical Ring^2)*Inner Semi Major Axis of Elliptical Ring)) to evaluate the Area of Elliptical Ring, Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes formula is defined as the total quantity of plane enclosed between the outer and inner elliptical boundary edges of the Elliptical Ring and calculated using the linear eccentricities and semi-major axes of the Elliptical Ring. Area of Elliptical Ring is denoted by A_Ring symbol.

How to evaluate Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes using this online evaluator? To use this online evaluator for Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes, enter Outer Semi Major Axis of Elliptical Ring (a_Outer), Outer Linear Eccentricity of Elliptical Ring (c_Outer), Inner Semi Major Axis of Elliptical Ring (a_Inner) & Inner Linear Eccentricity of Elliptical Ring (c_Inner) and hit the calculate button.

FAQs on Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes

What is the formula to find Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes?

The formula of Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes is expressed as Area of Elliptical Ring = pi*((sqrt(Outer Semi Major Axis of Elliptical Ring^2-Outer Linear Eccentricity of Elliptical Ring^2)*Outer Semi Major Axis of Elliptical Ring)-(sqrt(Inner Semi Major Axis of Elliptical Ring^2-Inner Linear Eccentricity of Elliptical Ring^2)*Inner Semi Major Axis of Elliptical Ring)). Here is an example- 124.9979 = pi*((sqrt(10^2-6^2)*10)-(sqrt(7^2-4^2)*7)).

How to calculate Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes?

With Outer Semi Major Axis of Elliptical Ring (a_Outer), Outer Linear Eccentricity of Elliptical Ring (c_Outer), Inner Semi Major Axis of Elliptical Ring (a_Inner) & Inner Linear Eccentricity of Elliptical Ring (c_Inner) we can find Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes using the formula - Area of Elliptical Ring = pi*((sqrt(Outer Semi Major Axis of Elliptical Ring^2-Outer Linear Eccentricity of Elliptical Ring^2)*Outer Semi Major Axis of Elliptical Ring)-(sqrt(Inner Semi Major Axis of Elliptical Ring^2-Inner Linear Eccentricity of Elliptical Ring^2)*Inner Semi Major Axis of Elliptical Ring)). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Area of Elliptical Ring?

Here are the different ways to Calculate Area of Elliptical Ring-

Area of Elliptical Ring=pi*((sqrt(Outer Semi Minor Axis of Elliptical Ring^2+Outer Linear Eccentricity of Elliptical Ring^2)*Outer Semi Minor Axis of Elliptical Ring)-(sqrt(Inner Semi Minor Axis of Elliptical Ring^2+Inner Linear Eccentricity of Elliptical Ring^2)*Inner Semi Minor Axis of Elliptical Ring))
Area of Elliptical Ring=pi*((Outer Semi Major Axis of Elliptical Ring*Outer Semi Minor Axis of Elliptical Ring)-((Outer Semi Major Axis of Elliptical Ring-Ring Width of Elliptical Ring)*(Outer Semi Minor Axis of Elliptical Ring-Ring Width of Elliptical Ring)))
Area of Elliptical Ring=pi*((Outer Semi Major Axis of Elliptical Ring*Outer Semi Minor Axis of Elliptical Ring)-(Inner Semi Major Axis of Elliptical Ring*Inner Semi Minor Axis of Elliptical Ring))

Can the Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes be negative?

No, the Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes, measured in Area cannot be negative.

Which unit is used to measure Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes?

Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes can be measured.

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Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes Formula

​GoArea of Elliptical Ring given Linear Eccentricities and Semi Minor Axes Formula

​GoArea of Elliptical Ring given Width and Outer Semi Axes Formula

Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes Example

Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes Solution

Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes Formula Elements

Other Formulas to find Area of Elliptical Ring

How to Evaluate Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes?

FAQs on Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes

Variable Name

GoArea of Elliptical Ring given Linear Eccentricities and Semi Minor Axes Formula

GoArea of Elliptical Ring given Width and Outer Semi Axes Formula