Total Surface Area of Toroid Sector given Volume and Angle of Intersection Calculator

✖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%
✖Volume of Toroid Sector is the amount of three dimensional space occupied by the Toroid Sector.ⓘ Volume of Toroid Sector [V_Sector]			+10% -10%

✖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 given Volume and Angle of Intersection [TSA_Sector]

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Formula

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Total Surface Area of Toroid Sector given Volume and Angle of Intersection

Formula

`"TSA"_{"Sector"} = ((2*pi*"r"*"P"_{"Cross Section"})*("∠"_{"Intersection"}/(2*pi)))+(2*("V"_{"Sector"}/(2*pi*"r"*("∠"_{"Intersection"}/(2*pi)))))`

Example

`"1042.427m²"=((2*pi*"10m"*"30m")*("180°"/(2*pi)))+(2*("1570m³"/(2*pi*"10m"*("180°"/(2*pi)))))`

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Total Surface Area of Toroid Sector given Volume and Angle of Intersection Solution

STEP 0: Pre-Calculation Summary

Formula Used

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*(Volume of Toroid Sector/(2*pi*Radius of Toroid*(Angle of Intersection of Toroid Sector/(2*pi)))))
TSA_Sector = ((2*pi*r*P_{Cross Section})*(∠_Intersection/(2*pi)))+(2*(V_Sector/(2*pi*r*(∠_Intersection/(2*pi)))))
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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.
Volume of Toroid Sector - (Measured in Cubic Meter) - Volume of Toroid Sector is the amount of three dimensional space occupied by the Toroid Sector.

STEP 1: Convert Input(s) to Base Unit

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)
Volume of Toroid Sector: 1570 Cubic Meter --> 1570 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA_Sector = ((2*pi*r*P_{Cross Section})*(∠_Intersection/(2*pi)))+(2*(V_Sector/(2*pi*r*(∠_Intersection/(2*pi))))) --> ((2*pi*10*30)*(3.1415926535892/(2*pi)))+(2*(1570/(2*pi*10*(3.1415926535892/(2*pi)))))

Evaluating ... ...

TSA_Sector = 1042.42710033849

STEP 3: Convert Result to Output's Unit

1042.42710033849 Square Meter --> No Conversion Required

FINAL ANSWER

1042.42710033849 ≈ 1042.427 Square Meter <-- Total Surface Area of Toroid Sector

(Calculation completed in 00.020 seconds)

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Home » Math » Geometry » 3D Geometry » Toroid » Toroid Sector » Total Surface Area of Toroid Sector » Total Surface Area of Toroid Sector given Volume and Angle of Intersection

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< 4 Total Surface Area of Toroid Sector Calculators

Total Surface Area of Toroid Sector given Volume of Toroid Sector

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

Total Surface Area of Toroid Sector given Volume and Angle of Intersection

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*(Volume of Toroid Sector/(2*pi*Radius of Toroid*(Angle of Intersection of Toroid Sector/(2*pi)))))

Total Surface Area of Toroid Sector given Volume

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)

Total Surface Area of Toroid Sector

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)

Total Surface Area of Toroid Sector given Volume and Angle of Intersection Formula

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 Total Surface Area of Toroid Sector given Volume and Angle of Intersection?

Total Surface Area of Toroid Sector given Volume and Angle of Intersection calculator uses 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*(Volume of Toroid Sector/(2*pi*Radius of Toroid*(Angle of Intersection of Toroid Sector/(2*pi))))) to calculate the Total Surface Area of Toroid Sector, Total Surface Area of Toroid Sector given Volume and Angle of Intersection formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Toroid Sector, calculated using volume and angle of intersection of Toroid Sector. Total Surface Area of Toroid Sector is denoted by TSA_Sector symbol.

How to calculate Total Surface Area of Toroid Sector given Volume and Angle of Intersection using this online calculator? To use this online calculator for Total Surface Area of Toroid Sector given Volume and Angle of Intersection, enter Radius of Toroid (r), Cross Sectional Perimeter of Toroid (P_{Cross Section}), Angle of Intersection of Toroid Sector (∠_Intersection) & Volume of Toroid Sector (V_Sector) and hit the calculate button. Here is how the Total Surface Area of Toroid Sector given Volume and Angle of Intersection calculation can be explained with given input values -> 1042.427 = ((2*pi*10*30)*(3.1415926535892/(2*pi)))+(2*(1570/(2*pi*10*(3.1415926535892/(2*pi))))).

FAQ

What is Total Surface Area of Toroid Sector given Volume and Angle of Intersection?

Total Surface Area of Toroid Sector given Volume and Angle of Intersection formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Toroid Sector, calculated using volume and angle of intersection of Toroid Sector and is represented as TSA_Sector = ((2*pi*r*P_{Cross Section})*(∠_Intersection/(2*pi)))+(2*(V_Sector/(2*pi*r*(∠_Intersection/(2*pi))))) or 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*(Volume of Toroid Sector/(2*pi*Radius of Toroid*(Angle of Intersection of Toroid Sector/(2*pi))))). 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 & Volume of Toroid Sector is the amount of three dimensional space occupied by the Toroid Sector.

How to calculate Total Surface Area of Toroid Sector given Volume and Angle of Intersection?

Total Surface Area of Toroid Sector given Volume and Angle of Intersection formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Toroid Sector, calculated using volume and angle of intersection of Toroid Sector is calculated using 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*(Volume of Toroid Sector/(2*pi*Radius of Toroid*(Angle of Intersection of Toroid Sector/(2*pi))))). To calculate Total Surface Area of Toroid Sector given Volume and Angle of Intersection, you need Radius of Toroid (r), Cross Sectional Perimeter of Toroid (P_{Cross Section}), Angle of Intersection of Toroid Sector (∠_Intersection) & Volume of Toroid Sector (V_Sector). With our tool, you need to enter the respective value for Radius of Toroid, Cross Sectional Perimeter of Toroid, Angle of Intersection of Toroid Sector & Volume 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 Total Surface Area of Toroid Sector?

In this formula, Total Surface Area of Toroid Sector uses Radius of Toroid, Cross Sectional Perimeter of Toroid, Angle of Intersection of Toroid Sector & Volume of Toroid Sector. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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