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

GoArea of Elliptical Ring given Width and Outer Semi Axes Formula

GoArea of Elliptical Ring 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{{b Outer}^{2} + {c Outer}^{2}} \cdot b Outer) - (\sqrt{{b Inner}^{2} + {c Inner}^{2}} \cdot b Inner))

A_Ring - Area of Elliptical Ring?b_Outer - Outer Semi Minor Axis of Elliptical Ring?c_Outer - Outer Linear Eccentricity of Elliptical Ring?b_Inner - Inner Semi Minor Axis of Elliptical Ring?c_Inner - Inner Linear Eccentricity of Elliptical Ring?π - Archimedes' constant?

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

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

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

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

150.7474 = 3.1416 \cdot ((\sqrt{8^{2} + 6^{2}} \cdot 8) - (\sqrt{5^{2} + 4^{2}} \cdot 5))

150.7474m² = 3.1416 \cdot ((\sqrt{{8m}^{2} + {6m}^{2}} \cdot 8m) - (\sqrt{{5m}^{2} + {4m}^{2}} \cdot 5m))

150.7474 = 3.1416 \cdot ((\sqrt{8^{2} + 6^{2}} \cdot 8) - (\sqrt{5^{2} + 4^{2}} \cdot 5))

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

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

A Ring = π \cdot ((\sqrt{{8m}^{2} + {6m}^{2}} \cdot 8m) - (\sqrt{{5m}^{2} + {4m}^{2}} \cdot 5m))

Next Step Substitute values of Constants

∴

A Ring = 3.1416 \cdot ((\sqrt{{8m}^{2} + {6m}^{2}} \cdot 8m) - (\sqrt{{5m}^{2} + {4m}^{2}} \cdot 5m))

Next Step Prepare to Evaluate

∴

A Ring = 3.1416 \cdot ((\sqrt{8^{2} + 6^{2}} \cdot 8) - (\sqrt{5^{2} + 4^{2}} \cdot 5))

Next Step Evaluate

∴

A Ring = 150.747371965475m²

LAST Step Rounding Answer

∴

A Ring = 150.7474m²

Area of Elliptical Ring given Linear Eccentricities and Semi Minor 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 Minor Axis of Elliptical Ring

Outer Semi Minor Axis of Elliptical Ring is half of the longest chord of the outer ellipse which is perpendicular to the line joining the foci of the outer ellipse of the Elliptical Ring.

Symbol: b_Outer

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Outer Semi Minor 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 Minor Axis of Elliptical Ring

Inner Semi Minor Axis of Elliptical Ring is half of the longest chord of the inner ellipse which is perpendicular to the line joining the foci of the inner ellipse of the Elliptical Ring.

Symbol: b_Inner

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inner Semi Minor 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 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))

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

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

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

Area of Elliptical Ring given Linear Eccentricities and Semi Minor Axes evaluator uses 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)) to evaluate the Area of Elliptical Ring, Area of Elliptical Ring given Linear Eccentricities and Semi Minor 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-minor 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 Minor Axes using this online evaluator? To use this online evaluator for Area of Elliptical Ring given Linear Eccentricities and Semi Minor Axes, enter Outer Semi Minor Axis of Elliptical Ring (b_Outer), Outer Linear Eccentricity of Elliptical Ring (c_Outer), Inner Semi Minor Axis of Elliptical Ring (b_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 Minor Axes

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

The formula of Area of Elliptical Ring given Linear Eccentricities and Semi Minor Axes is expressed as 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)). Here is an example- 150.7474 = pi*((sqrt(8^2+6^2)*8)-(sqrt(5^2+4^2)*5)).

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

With Outer Semi Minor Axis of Elliptical Ring (b_Outer), Outer Linear Eccentricity of Elliptical Ring (c_Outer), Inner Semi Minor Axis of Elliptical Ring (b_Inner) & Inner Linear Eccentricity of Elliptical Ring (c_Inner) we can find Area of Elliptical Ring given Linear Eccentricities and Semi Minor Axes using the formula - 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)). 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*((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))
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))

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

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

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

Area of Elliptical Ring given Linear Eccentricities and Semi Minor 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 Minor Axes can be measured.

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

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

​GoArea of Elliptical Ring Formula

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

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

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

Other Formulas to find Area of Elliptical Ring

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

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

Variable Name

GoArea of Elliptical Ring given Width and Outer Semi Axes Formula

GoArea of Elliptical Ring Formula