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Volume of Toroid Sector Formula

GoVolume of Toroid Sector given Total Surface Area Formula

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Volume of Toroid Sector is the amount of three dimensional space occupied by the Toroid Sector. Check FAQs

V Sector = (2 \cdot π \cdot r \cdot A Cross Section) \cdot (\frac{∠ Intersection}{2 \cdot π})

V_Sector - Volume of Toroid Sector?r - Radius of Toroid?A_{Cross Section} - Cross Sectional Area of Toroid?∠_Intersection - Angle of Intersection of Toroid Sector?π - Archimedes' constant?

Volume of Toroid Sector Example

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Here is how the Volume of Toroid Sector equation looks like with Values.

Here is how the Volume of Toroid Sector equation looks like with Units.

Here is how the Volume of Toroid Sector equation looks like.

1570.7963 = (2 \cdot 3.1416 \cdot 10 \cdot 50) \cdot (\frac{180}{2 \cdot 3.1416})

1570.7963m³ = (2 \cdot 3.1416 \cdot 10m \cdot 50m²) \cdot (\frac{180°}{2 \cdot 3.1416})

1570.7963 = (2 \cdot 3.1416 \cdot 10 \cdot 50) \cdot (\frac{180}{2 \cdot 3.1416})

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Home » Math » Geometry » 3D Geometry » Volume of Toroid Sector

Volume of Toroid Sector Solution

Follow our step by step solution on how to calculate Volume of Toroid Sector?

FIRST Step Consider the formula

V Sector = (2 \cdot π \cdot r \cdot A Cross Section) \cdot (\frac{∠ Intersection}{2 \cdot π})

Next Step Substitute values of Variables

∴

V Sector = (2 \cdot π \cdot 10m \cdot 50m²) \cdot (\frac{180°}{2 \cdot π})

Next Step Substitute values of Constants

∴

V Sector = (2 \cdot 3.1416 \cdot 10m \cdot 50m²) \cdot (\frac{180°}{2 \cdot 3.1416})

Next Step Convert Units

∴

V Sector = (2 \cdot 3.1416 \cdot 10m \cdot 50m²) \cdot (\frac{3.1416rad}{2 \cdot 3.1416})

Next Step Prepare to Evaluate

∴

V Sector = (2 \cdot 3.1416 \cdot 10 \cdot 50) \cdot (\frac{3.1416}{2 \cdot 3.1416})

Next Step Evaluate

∴

V Sector = 1570.7963267946m³

LAST Step Rounding Answer

∴

V Sector = 1570.7963m³

Volume of Toroid Sector Formula Elements

Variables

Constants

Volume of Toroid Sector

Volume of Toroid Sector is the amount of three dimensional space occupied by the Toroid Sector.

Symbol: V_Sector

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Radius of Toroid

Radius of Toroid is the line connecting the center of the overall Toroid to the center of a cross-section of the Toroid.

Symbol: r

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Cross Sectional Area of Toroid

Cross Sectional Area of Toroid is the amount of two-dimensional space occupied by the cross-section of the Toroid.

Symbol: A_{Cross Section}

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Angle of Intersection of Toroid Sector

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.

Symbol: ∠_Intersection

Measurement: AngleUnit: °

Note: Value should be between 0 to 360.

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Credits

Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has created this Formula and 2500+ more formulas!

Verified by Mona Gladys

St Joseph's College (SJC), Bengaluru

Mona Gladys has verified this Formula and 1800+ more formulas!

Other Formulas to find Volume of Toroid Sector

Go Volume of Toroid Sector given Total Surface Area

V Sector = (2 \cdot π \cdot A Cross Section) \cdot ((\frac{TSA Sector - (2 \cdot A Cross Section)}{2 \cdot π \cdot P Cross Section}))

Other formulas in Volume of Toroid Sector category

Go Total Surface Area of Toroid Sector

TSA Sector = ((2 \cdot π \cdot r \cdot P Cross Section) \cdot (\frac{∠ Intersection}{2 \cdot π})) + (2 \cdot A Cross Section)

Go Total Surface Area of Toroid Sector given Volume

TSA Sector = ((2 \cdot π \cdot P Cross Section) \cdot ((\frac{V Sector}{2 \cdot π \cdot A Cross Section}))) + (2 \cdot A Cross Section)

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

A Cross Section = (\frac{TSA Sector - (2 \cdot π \cdot r \cdot P Cross Section \cdot (\frac{∠ Intersection}{2 \cdot π}))}{2})

Go Cross Sectional Area of Toroid given Volume of Toroid Sector

A Cross Section = (\frac{V Sector}{2 \cdot π \cdot r \cdot (\frac{∠ Intersection}{2 \cdot π})})

How to Evaluate Volume of Toroid Sector?

Volume of Toroid Sector evaluator uses Volume of Toroid Sector = (2*pi*Radius of Toroid*Cross Sectional Area of Toroid)*(Angle of Intersection of Toroid Sector/(2*pi)) to evaluate 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 evaluate Volume of Toroid Sector using this online evaluator? To use this online evaluator 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.

FAQs on Volume of Toroid Sector

What is the formula to find Volume of Toroid Sector?

The formula of Volume of Toroid Sector is expressed as Volume of Toroid Sector = (2*pi*Radius of Toroid*Cross Sectional Area of Toroid)*(Angle of Intersection of Toroid Sector/(2*pi)). Here is an example- 1570.796 = (2*pi*10*50)*(3.1415926535892/(2*pi)).

How to calculate Volume of Toroid Sector?

With Radius of Toroid (r), Cross Sectional Area of Toroid (A_{Cross Section}) & Angle of Intersection of Toroid Sector (∠_Intersection) we can find Volume of Toroid Sector using the formula - Volume of Toroid Sector = (2*pi*Radius of Toroid*Cross Sectional Area of Toroid)*(Angle of Intersection of Toroid Sector/(2*pi)). This formula also uses Archimedes' constant .

What are the other ways to Calculate Volume of Toroid Sector?

Here are the different ways to Calculate Volume of Toroid Sector-

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)))

Can the Volume of Toroid Sector be negative?

No, the Volume of Toroid Sector, measured in Volume cannot be negative.

Which unit is used to measure Volume of Toroid Sector?

Volume of Toroid Sector is usually measured using the Cubic Meter[m³] for Volume. Cubic Centimeter[m³], Cubic Millimeter[m³], Liter[m³] are the few other units in which Volume of Toroid Sector can be measured.