Volume of Toroid Sector given Base Area 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%
✖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%
✖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 given Base Area [V_Sector]

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Formula

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Volume of Toroid Sector given Base Area

Formula

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

Example

`"1583.333m³"=(2*pi*(("1050m²"-(2*"50m²"))/(2*pi*"30m"*("180°"/(2*pi))))*"50m²")*("180°"/(2*pi))`

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Volume of Toroid Sector given Base Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
V_Sector = (2*pi*((TSA_Sector-(2*A_{Cross Section}))/(2*pi*P_{Cross Section}*(∠_Intersection/(2*pi))))*A_{Cross Section})*(∠_Intersection/(2*pi))
This formula uses 1 Constants, 5 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.
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.
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.
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
Cross Sectional Area of Toroid: 50 Square Meter --> 50 Square 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

V_Sector = (2*pi*((TSA_Sector-(2*A_{Cross Section}))/(2*pi*P_{Cross Section}*(∠_Intersection/(2*pi))))*A_{Cross Section})*(∠_Intersection/(2*pi)) --> (2*pi*((1050-(2*50))/(2*pi*30*(3.1415926535892/(2*pi))))*50)*(3.1415926535892/(2*pi))

Evaluating ... ...

V_Sector = 1583.33333333333

STEP 3: Convert Result to Output's Unit

1583.33333333333 Cubic Meter --> No Conversion Required

FINAL ANSWER

1583.33333333333 ≈ 1583.333 Cubic Meter <-- Volume of Toroid Sector

(Calculation completed in 00.004 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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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))

Volume of Toroid Sector given Base Area Formula

What is Toroid?

In mathematics, a Toroid is a surface of revolution with a hole in the middle, like a doughnut, forming a solid body. The axis of revolution passes through the hole and so does not intersect the surface.

How to Calculate Volume of Toroid Sector given Base Area?

Volume of Toroid Sector given Base Area calculator uses 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)) to calculate the Volume of Toroid Sector, Volume of Toroid Sector given Base Area formula is defined as the amount of three-dimensional space occupied by Toroid sector, calculated using base area of Toroid. Volume of Toroid Sector is denoted by V_Sector symbol.

How to calculate Volume of Toroid Sector given Base Area using this online calculator? To use this online calculator for Volume of Toroid Sector given Base Area, enter Total Surface Area of Toroid Sector (TSA_Sector), Cross Sectional Area of Toroid (A_{Cross Section}), Cross Sectional Perimeter of Toroid (P_{Cross Section}) & Angle of Intersection of Toroid Sector (∠_Intersection) and hit the calculate button. Here is how the Volume of Toroid Sector given Base Area calculation can be explained with given input values -> 1583.333 = (2*pi*((1050-(2*50))/(2*pi*30*(3.1415926535892/(2*pi))))*50)*(3.1415926535892/(2*pi)).

FAQ

What is Volume of Toroid Sector given Base Area?

Volume of Toroid Sector given Base Area formula is defined as the amount of three-dimensional space occupied by Toroid sector, calculated using base area of Toroid and is represented as V_Sector = (2*pi*((TSA_Sector-(2*A_{Cross Section}))/(2*pi*P_{Cross Section}*(∠_Intersection/(2*pi))))*A_{Cross Section})*(∠_Intersection/(2*pi)) or 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)). Total Surface Area of Toroid Sector is the total quantity of two-dimensional space enclosed on the entire surface of the Toroid Sector, Cross Sectional Area of Toroid is the amount of two-dimensional space occupied by the 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 Volume of Toroid Sector given Base Area?

Volume of Toroid Sector given Base Area formula is defined as the amount of three-dimensional space occupied by Toroid sector, calculated using base area of Toroid is calculated using 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)). To calculate Volume of Toroid Sector given Base Area, you need Total Surface Area of Toroid Sector (TSA_Sector), Cross Sectional Area of Toroid (A_{Cross Section}), 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, Cross Sectional Area 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 Volume of Toroid Sector?

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

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 = (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))

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