Volume of Toroid Sector 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 Area of Toroid is the amount of two-dimensional space occupied by the cross-section of the Toroid.ⓘ Cross Sectional Area of Toroid [A_{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]

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Formula

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Volume of Toroid Sector

Formula

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

Example

`"1570.796m³"=(2*pi*"10m"*"50m²")*("180°"/(2*pi))`

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Volume of Toroid Sector Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Toroid Sector = (2*pi*Radius of Toroid*Cross Sectional Area of Toroid)*(Angle of Intersection of Toroid Sector/(2*pi))
V_Sector = (2*pi*r*A_{Cross Section})*(∠_Intersection/(2*pi))
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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

Radius of Toroid: 10 Meter --> 10 Meter No Conversion Required
Cross Sectional Area of Toroid: 50 Square Meter --> 50 Square 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

V_Sector = (2*pi*r*A_{Cross Section})*(∠_Intersection/(2*pi)) --> (2*pi*10*50)*(3.1415926535892/(2*pi))

Evaluating ... ...

V_Sector = 1570.7963267946

STEP 3: Convert Result to Output's Unit

1570.7963267946 Cubic Meter --> No Conversion Required

FINAL ANSWER

1570.7963267946 ≈ 1570.796 Cubic Meter <-- Volume of Toroid Sector

(Calculation completed in 00.004 seconds)

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< 4 Volume of Toroid Sector Calculators

Volume of Toroid Sector given Base Area

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

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

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

Volume of Toroid Sector given Total Surface Area

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)))

Volume of Toroid Sector

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

< 7 Toroid Sector Calculators

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)

Volume of Toroid Sector given Total Surface Area

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)))

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

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

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)

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)

Cross Sectional Area of Toroid given Volume of Toroid Sector

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

Volume of Toroid Sector

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

Volume of Toroid Sector Formula

Volume of Toroid Sector = (2*pi*Radius of Toroid*Cross Sectional Area of Toroid)*(Angle of Intersection of Toroid Sector/(2*pi))
V_Sector = (2*pi*r*A_{Cross Section})*(∠_Intersection/(2*pi))

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 Volume of Toroid Sector?

Volume of Toroid Sector calculator uses Volume of Toroid Sector = (2*pi*Radius of Toroid*Cross Sectional Area of Toroid)*(Angle of Intersection of Toroid Sector/(2*pi)) to calculate the Volume of Toroid Sector, The Volume of Toroid Sector formula is defined as the amount of three dimensional space occupied by Toroid sector. Volume of Toroid Sector is denoted by V_Sector symbol.

How to calculate Volume of Toroid Sector using this online calculator? To use this online calculator for Volume of Toroid Sector, enter Radius of Toroid (r), Cross Sectional Area of Toroid (A_{Cross Section}) & Angle of Intersection of Toroid Sector (∠_Intersection) and hit the calculate button. Here is how the Volume of Toroid Sector calculation can be explained with given input values -> 1570.796 = (2*pi*10*50)*(3.1415926535892/(2*pi)).

FAQ

What is Volume of Toroid Sector?

The Volume of Toroid Sector formula is defined as the amount of three dimensional space occupied by Toroid sector and is represented as V_Sector = (2*pi*r*A_{Cross Section})*(∠_Intersection/(2*pi)) or Volume of Toroid Sector = (2*pi*Radius of Toroid*Cross Sectional Area 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 Area of Toroid is the amount of two-dimensional space occupied by 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 Volume of Toroid Sector?

The Volume of Toroid Sector formula is defined as the amount of three dimensional space occupied by Toroid sector is calculated using Volume of Toroid Sector = (2*pi*Radius of Toroid*Cross Sectional Area of Toroid)*(Angle of Intersection of Toroid Sector/(2*pi)). To calculate Volume of Toroid Sector, you need Radius of Toroid (r), Cross Sectional Area of Toroid (A_{Cross Section}) & Angle of Intersection of Toroid Sector (∠_Intersection). With our tool, you need to enter the respective value for Radius of Toroid, Cross Sectional Area 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 Volume of Toroid Sector?

In this formula, Volume of Toroid Sector uses Radius of Toroid, Cross Sectional Area of Toroid & Angle of Intersection of Toroid Sector. We can use 4 other way(s) to calculate the same, which is/are as follows -

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

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