Area of Elliptical Ring given Width and Outer Semi Axes Calculator

✖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.ⓘ Outer Semi Major Axis of Elliptical Ring [a_Outer]			+10% -10%
✖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.ⓘ Outer Semi Minor Axis of Elliptical Ring [b_Outer]			+10% -10%
✖Ring Width of Elliptical Ring is the perpendicular distance between outer and inner ellipses of the Elliptical Ring.ⓘ Ring Width of Elliptical Ring [w_Ring]			+10% -10%

✖Area of Elliptical Ring is the total quantity of plane enclosed between the outer and inner elliptical boundary edges of the Elliptical Ring.ⓘ Area of Elliptical Ring given Width and Outer Semi Axes [A_Ring]

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Area of Elliptical Ring given Width and Outer Semi Axes Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
A_Ring = pi*((a_Outer*b_Outer)-((a_Outer-w_Ring)*(b_Outer-w_Ring)))
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Area of Elliptical Ring - (Measured in Square Meter) - Area of Elliptical Ring is the total quantity of plane enclosed between the outer and inner elliptical boundary edges of the Elliptical Ring.
Outer Semi Major Axis of Elliptical Ring - (Measured in Meter) - 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.
Outer Semi Minor Axis of Elliptical Ring - (Measured in Meter) - 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.
Ring Width of Elliptical Ring - (Measured in Meter) - Ring Width of Elliptical Ring is the perpendicular distance between outer and inner ellipses of the Elliptical Ring.

STEP 1: Convert Input(s) to Base Unit

Outer Semi Major Axis of Elliptical Ring: 10 Meter --> 10 Meter No Conversion Required
Outer Semi Minor Axis of Elliptical Ring: 8 Meter --> 8 Meter No Conversion Required
Ring Width of Elliptical Ring: 3 Meter --> 3 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A_Ring = pi*((a_Outer*b_Outer)-((a_Outer-w_Ring)*(b_Outer-w_Ring))) --> pi*((10*8)-((10-3)*(8-3)))

Evaluating ... ...

A_Ring = 141.371669411541

STEP 3: Convert Result to Output's Unit

141.371669411541 Square Meter --> No Conversion Required

FINAL ANSWER

141.371669411541 ≈ 141.3717 Square Meter <-- Area of Elliptical Ring

(Calculation completed in 00.020 seconds)

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< Area of Elliptical Ring Calculators

Area of Elliptical Ring given Linear Eccentricities and Semi Minor Axes

LaTeX Go 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 given Linear Eccentricities and Semi Major Axes

LaTeX Go 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))

Area of Elliptical Ring given Width and Outer Semi Axes

LaTeX Go 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

LaTeX Go 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 given Width and Outer Semi Axes Formula

LaTeX Go

What is an Elliptical Ring?

An Elliptical Ring is an ellipse in which another smaller ellipse is removed from the center, such that the difference of inner and outer semi axes (semi major axes and semi minor axes) are equal. That difference is called the width of the Elliptical Ring.

What is an Ellipse?

An Ellipse is basically a conic section. If we cut a right circular cone using a plane at an angle greater than the semi angle of cone. Geometrically an Ellipse is the collection of all points in a plane such that the sum of the distances to them from two fixed points is a constant. Those fixed points are the foci of the Ellipse. The largest chord of the Ellipse is the major axis and the chord which passing through the center and perpendicular to the major axis is the minor axis of the ellipse. Circle is a special case of Ellipse in which both foci coincide at the center and so both major and minor axes become equal in length which is called the diameter of the circle.

How to Calculate Area of Elliptical Ring given Width and Outer Semi Axes?

Area of Elliptical Ring given Width and Outer Semi Axes calculator uses 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))) to calculate the Area of Elliptical Ring, Area of Elliptical Ring given Width and Outer Semi 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 width and outer semi-axes of the Elliptical Ring. Area of Elliptical Ring is denoted by A_Ring symbol.

How to calculate Area of Elliptical Ring given Width and Outer Semi Axes using this online calculator? To use this online calculator for Area of Elliptical Ring given Width and Outer Semi Axes, enter Outer Semi Major Axis of Elliptical Ring (a_Outer), Outer Semi Minor Axis of Elliptical Ring (b_Outer) & Ring Width of Elliptical Ring (w_Ring) and hit the calculate button. Here is how the Area of Elliptical Ring given Width and Outer Semi Axes calculation can be explained with given input values -> 141.3717 = pi*((10*8)-((10-3)*(8-3))).

FAQ

What is Area of Elliptical Ring given Width and Outer Semi Axes?

Area of Elliptical Ring given Width and Outer Semi 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 width and outer semi-axes of the Elliptical Ring and is represented as A_Ring = pi*((a_Outer*b_Outer)-((a_Outer-w_Ring)*(b_Outer-w_Ring))) or 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))). 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, 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 & Ring Width of Elliptical Ring is the perpendicular distance between outer and inner ellipses of the Elliptical Ring.

How to calculate Area of Elliptical Ring given Width and Outer Semi Axes?

Area of Elliptical Ring given Width and Outer Semi 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 width and outer semi-axes of the Elliptical Ring is calculated using 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))). To calculate Area of Elliptical Ring given Width and Outer Semi Axes, you need Outer Semi Major Axis of Elliptical Ring (a_Outer), Outer Semi Minor Axis of Elliptical Ring (b_Outer) & Ring Width of Elliptical Ring (w_Ring). With our tool, you need to enter the respective value for Outer Semi Major Axis of Elliptical Ring, Outer Semi Minor Axis of Elliptical Ring & Ring Width of Elliptical Ring 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 Elliptical Ring?

In this formula, Area of Elliptical Ring uses Outer Semi Major Axis of Elliptical Ring, Outer Semi Minor Axis of Elliptical Ring & Ring Width of Elliptical Ring. We can use 3 other way(s) to calculate the same, which is/are as follows -

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)-(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))

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