Cross Sectional Area of Toroid given Total Surface Area of Toroid Sector Calculator

✖Total Surface Area of Toroid Sector is the total quantity of two-dimensional space enclosed on the entire surface of the Toroid Sector.ⓘ Total Surface Area of Toroid Sector [TSA_Sector]			+10% -10%
✖Radius of Toroid is the line connecting the center of the overall Toroid to the center of a cross-section of the Toroid.ⓘ Radius of Toroid [r]			+10% -10%
✖Cross Sectional Perimeter of Toroid is the total length of the boundary of the cross-section of the Toroid.ⓘ Cross Sectional Perimeter of Toroid [P_{Cross Section}]			+10% -10%
✖Angle of Intersection of Toroid Sector is the angle subtended by the planes in which each of the circular end faces of the Toroid Sector is contained.ⓘ Angle of Intersection of Toroid Sector [∠_Intersection]			+10% -10%

✖Cross Sectional Area of Toroid is the amount of two-dimensional space occupied by the cross-section of the Toroid.ⓘ Cross Sectional Area of Toroid given Total Surface Area of Toroid Sector [A_{Cross Section}]

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Cross Sectional Area of Toroid given Total Surface Area of Toroid Sector Solution

STEP 0: Pre-Calculation Summary

Formula Used

Cross Sectional Area of Toroid = ((Total Surface Area of Toroid Sector-(2*pi*Radius of Toroid*Cross Sectional Perimeter of Toroid*(Angle of Intersection of Toroid Sector/(2*pi))))/2)
A_{Cross Section} = ((TSA_Sector-(2*pi*r*P_{Cross Section}*(∠_Intersection/(2*pi))))/2)
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Cross Sectional Area of Toroid - (Measured in Square Meter) - Cross Sectional Area of Toroid is the amount of two-dimensional space occupied by the cross-section of the Toroid.
Total Surface Area of Toroid Sector - (Measured in Square Meter) - Total Surface Area of Toroid Sector is the total quantity of two-dimensional space enclosed on the entire surface of the Toroid Sector.
Radius of Toroid - (Measured in Meter) - Radius of Toroid is the line connecting the center of the overall Toroid to the center of a cross-section of the Toroid.
Cross Sectional Perimeter of Toroid - (Measured in Meter) - Cross Sectional Perimeter of Toroid is the total length of the boundary of the cross-section of the Toroid.
Angle of Intersection of Toroid Sector - (Measured in Radian) - Angle of Intersection of Toroid Sector is the angle subtended by the planes in which each of the circular end faces of the Toroid Sector is contained.

STEP 1: Convert Input(s) to Base Unit

Total Surface Area of Toroid Sector: 1050 Square Meter --> 1050 Square Meter No Conversion Required
Radius of Toroid: 10 Meter --> 10 Meter No Conversion Required
Cross Sectional Perimeter of Toroid: 30 Meter --> 30 Meter No Conversion Required
Angle of Intersection of Toroid Sector: 180 Degree --> 3.1415926535892 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A_{Cross Section} = ((TSA_Sector-(2*pi*r*P_{Cross Section}*(∠_Intersection/(2*pi))))/2) --> ((1050-(2*pi*10*30*(3.1415926535892/(2*pi))))/2)

Evaluating ... ...

A_{Cross Section} = 53.7611019616201

STEP 3: Convert Result to Output's Unit

53.7611019616201 Square Meter --> No Conversion Required

FINAL ANSWER

53.7611019616201 ≈ 53.7611 Square Meter <-- Cross Sectional Area of Toroid

(Calculation completed in 00.007 seconds)

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< Toroid Sector Calculators

Cross Sectional Perimeter of Toroid given Total Surface Area of Toroid Sector

LaTeX Go Cross Sectional Perimeter of Toroid = (Total Surface Area of Toroid Sector-(2*Cross Sectional Area of Toroid))/(2*pi*Radius of Toroid*(Angle of Intersection of Toroid Sector/(2*pi)))

Cross Sectional Area of Toroid given Total Surface Area of Toroid Sector

LaTeX Go Cross Sectional Area of Toroid = ((Total Surface Area of Toroid Sector-(2*pi*Radius of Toroid*Cross Sectional Perimeter of Toroid*(Angle of Intersection of Toroid Sector/(2*pi))))/2)

Radius of Toroid given Total Surface Area of Toroid Sector

LaTeX Go Radius of Toroid = (Total Surface Area of Toroid Sector-(2*Cross Sectional Area of Toroid))/(2*pi*Cross Sectional Perimeter of Toroid*(Angle of Intersection of Toroid Sector/(2*pi)))

Cross Sectional Area of Toroid given Volume of Toroid Sector

LaTeX Go Cross Sectional Area of Toroid = (Volume of Toroid Sector/(2*pi*Radius of Toroid*(Angle of Intersection of Toroid Sector/(2*pi))))

< Toroid Sector Calculators

Total Surface Area of Toroid Sector given Volume

LaTeX Go Total Surface Area of Toroid Sector = ((2*pi*Cross Sectional Perimeter of Toroid)*((Volume of Toroid Sector/(2*pi*Cross Sectional Area of Toroid))))+(2*Cross Sectional Area of Toroid)

Volume of Toroid Sector given Total Surface Area

LaTeX Go Volume of Toroid Sector = (2*pi*Cross Sectional Area of Toroid)*(((Total Surface Area of Toroid Sector-(2*Cross Sectional Area of Toroid))/(2*pi*Cross Sectional Perimeter of Toroid)))

Total Surface Area of Toroid Sector

LaTeX Go Total Surface Area of Toroid Sector = ((2*pi*Radius of Toroid*Cross Sectional Perimeter of Toroid)*(Angle of Intersection of Toroid Sector/(2*pi)))+(2*Cross Sectional Area of Toroid)

Volume of Toroid Sector

LaTeX Go Volume of Toroid Sector = (2*pi*Radius of Toroid*Cross Sectional Area of Toroid)*(Angle of Intersection of Toroid Sector/(2*pi))

Cross Sectional Area of Toroid given Total Surface Area of Toroid Sector Formula

LaTeX Go

What is Toroid Sector?

Toroid Sector is a piece cut straight out of a toroid. The size of the piece is determined by the angle of intersection originating at the center. An angle of 360° covers the whole toroid.

What is Toroid?

In geometry, a Toroid is a surface of revolution with a hole in the middle. The axis of revolution passes through the hole and so does not intersect the surface. For example, when a rectangle is rotated around an axis parallel to one of its edges, then a hollow rectangle-section ring is produced. If the revolved figure is a circle, then the object is called a torus.

How to Calculate Cross Sectional Area of Toroid given Total Surface Area of Toroid Sector?

Cross Sectional Area of Toroid given Total Surface Area of Toroid Sector calculator uses Cross Sectional Area of Toroid = ((Total Surface Area of Toroid Sector-(2*pi*Radius of Toroid*Cross Sectional Perimeter of Toroid*(Angle of Intersection of Toroid Sector/(2*pi))))/2) to calculate the Cross Sectional Area of Toroid, Cross Sectional Area of Toroid given Total Surface Area of Toroid Sector formula is defined as the amount of two dimensional space occupied by the cross section of Toroid, calculated using total surface area of Toroid Sector. Cross Sectional Area of Toroid is denoted by A_{Cross Section} symbol.

How to calculate Cross Sectional Area of Toroid given Total Surface Area of Toroid Sector using this online calculator? To use this online calculator for Cross Sectional Area of Toroid given Total Surface Area of Toroid Sector, enter Total Surface Area of Toroid Sector (TSA_Sector), Radius of Toroid (r), Cross Sectional Perimeter of Toroid (P_{Cross Section}) & Angle of Intersection of Toroid Sector (∠_Intersection) and hit the calculate button. Here is how the Cross Sectional Area of Toroid given Total Surface Area of Toroid Sector calculation can be explained with given input values -> 53.7611 = ((1050-(2*pi*10*30*(3.1415926535892/(2*pi))))/2).

FAQ

What is Cross Sectional Area of Toroid given Total Surface Area of Toroid Sector?

Cross Sectional Area of Toroid given Total Surface Area of Toroid Sector formula is defined as the amount of two dimensional space occupied by the cross section of Toroid, calculated using total surface area of Toroid Sector and is represented as A_{Cross Section} = ((TSA_Sector-(2*pi*r*P_{Cross Section}*(∠_Intersection/(2*pi))))/2) or Cross Sectional Area of Toroid = ((Total Surface Area of Toroid Sector-(2*pi*Radius of Toroid*Cross Sectional Perimeter of Toroid*(Angle of Intersection of Toroid Sector/(2*pi))))/2). Total Surface Area of Toroid Sector is the total quantity of two-dimensional space enclosed on the entire surface of the Toroid Sector, Radius of Toroid is the line connecting the center of the overall Toroid to the center of a cross-section of the Toroid, Cross Sectional Perimeter of Toroid is the total length of the boundary of the cross-section of the Toroid & Angle of Intersection of Toroid Sector is the angle subtended by the planes in which each of the circular end faces of the Toroid Sector is contained.

How to calculate Cross Sectional Area of Toroid given Total Surface Area of Toroid Sector?

Cross Sectional Area of Toroid given Total Surface Area of Toroid Sector formula is defined as the amount of two dimensional space occupied by the cross section of Toroid, calculated using total surface area of Toroid Sector is calculated using Cross Sectional Area of Toroid = ((Total Surface Area of Toroid Sector-(2*pi*Radius of Toroid*Cross Sectional Perimeter of Toroid*(Angle of Intersection of Toroid Sector/(2*pi))))/2). To calculate Cross Sectional Area of Toroid given Total Surface Area of Toroid Sector, you need Total Surface Area of Toroid Sector (TSA_Sector), Radius of Toroid (r), Cross Sectional Perimeter of Toroid (P_{Cross Section}) & Angle of Intersection of Toroid Sector (∠_Intersection). With our tool, you need to enter the respective value for Total Surface Area of Toroid Sector, Radius of Toroid, Cross Sectional Perimeter of Toroid & Angle of Intersection of Toroid Sector 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 Cross Sectional Area of Toroid?

In this formula, Cross Sectional Area of Toroid uses Total Surface Area of Toroid Sector, Radius of Toroid, Cross Sectional Perimeter of Toroid & Angle of Intersection of Toroid Sector. We can use 2 other way(s) to calculate the same, which is/are as follows -

Cross Sectional Area of Toroid = (Volume of Toroid Sector/(2*pi*Radius of Toroid*(Angle of Intersection of Toroid Sector/(2*pi))))
Cross Sectional Area of Toroid = (Volume of Toroid Sector/(2*pi*Radius of Toroid*(Angle of Intersection of Toroid Sector/(2*pi))))

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