Volume of Toroid Sector given Total Surface Area Calculator

✖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%
✖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 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%

✖Volume of Toroid Sector is the amount of three dimensional space occupied by the Toroid Sector.ⓘ Volume of Toroid Sector given Total Surface Area [V_Sector]

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Volume of Toroid Sector given Total Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
V_Sector = (2*pi*A_{Cross Section})*(((TSA_Sector-(2*A_{Cross Section}))/(2*pi*P_{Cross Section})))
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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Cross Sectional Area of Toroid: 50 Square Meter --> 50 Square Meter No Conversion Required
Total Surface Area of Toroid Sector: 1050 Square Meter --> 1050 Square Meter No Conversion Required
Cross Sectional Perimeter of Toroid: 30 Meter --> 30 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

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

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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< Volume of Toroid Sector Calculators

Volume of Toroid Sector given Base Area

LaTeX 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

LaTeX 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

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)))

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))

< 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))

Volume of Toroid Sector given Total Surface Area 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 Volume of Toroid Sector given Total Surface Area?

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

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

FAQ

What is Volume of Toroid Sector given Total Surface Area?

Volume of Toroid Sector given Total Surface Area of Toroid Sector formula is defined as the amount of three-dimensional space occupied by Toroid sector, calculated using total surface area of Toroid Sector and is represented as V_Sector = (2*pi*A_{Cross Section})*(((TSA_Sector-(2*A_{Cross Section}))/(2*pi*P_{Cross Section}))) or 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 Area of Toroid is the amount of two-dimensional space occupied by the cross-section of the Toroid, 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 Perimeter of Toroid is the total length of the boundary of the cross-section of the Toroid.

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

Volume of Toroid Sector given Total Surface Area of Toroid Sector formula is defined as the amount of three-dimensional space occupied by Toroid sector, calculated using total surface area of Toroid Sector is calculated using 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))). To calculate Volume of Toroid Sector given Total Surface Area, you need Cross Sectional Area of Toroid (A_{Cross Section}), Total Surface Area of Toroid Sector (TSA_Sector) & Cross Sectional Perimeter of Toroid (P_{Cross Section}). With our tool, you need to enter the respective value for Cross Sectional Area of Toroid, Total Surface Area of Toroid Sector & Cross Sectional Perimeter of Toroid 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 Cross Sectional Area of Toroid, Total Surface Area of Toroid Sector & Cross Sectional Perimeter of Toroid. 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*((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*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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