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

GoVolume of Toroid Sector Formula

GoVolume of Toroid Sector given Base 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 (\frac{TSA Sector - (2 \cdot π \cdot r \cdot P Cross Section \cdot (\frac{∠ Intersection}{2 \cdot π}))}{2})) \cdot (\frac{∠ Intersection}{2 \cdot π})

V_Sector - Volume of Toroid Sector?r - Radius of Toroid?TSA_Sector - Total Surface Area of Toroid Sector?P_{Cross Section} - Cross Sectional Perimeter of Toroid?∠_Intersection - Angle of Intersection of Toroid Sector?π - Archimedes' constant?

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

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Here is how the Volume of Toroid Sector given Total Surface Area and Angle of Intersection equation looks like with Values.

Here is how the Volume of Toroid Sector given Total Surface Area and Angle of Intersection equation looks like with Units.

Here is how the Volume of Toroid Sector given Total Surface Area and Angle of Intersection equation looks like.

1688.9548 = (2 \cdot 3.1416 \cdot 10 \cdot (\frac{1050 - (2 \cdot 3.1416 \cdot 10 \cdot 30 \cdot (\frac{180}{2 \cdot 3.1416}))}{2})) \cdot (\frac{180}{2 \cdot 3.1416})

1688.9548m³ = (2 \cdot 3.1416 \cdot 10m \cdot (\frac{1050m² - (2 \cdot 3.1416 \cdot 10m \cdot 30m \cdot (\frac{180°}{2 \cdot 3.1416}))}{2})) \cdot (\frac{180°}{2 \cdot 3.1416})

1688.9548 = (2 \cdot 3.1416 \cdot 10 \cdot (\frac{1050 - (2 \cdot 3.1416 \cdot 10 \cdot 30 \cdot (\frac{180}{2 \cdot 3.1416}))}{2})) \cdot (\frac{180}{2 \cdot 3.1416})

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

Follow our step by step solution on how to calculate Volume of Toroid Sector given Total Surface Area and Angle of Intersection?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

V Sector = (2 \cdot π \cdot 10m \cdot (\frac{1050m² - (2 \cdot π \cdot 10m \cdot 30m \cdot (\frac{180°}{2 \cdot π}))}{2})) \cdot (\frac{180°}{2 \cdot π})

Next Step Substitute values of Constants

∴

V Sector = (2 \cdot 3.1416 \cdot 10m \cdot (\frac{1050m² - (2 \cdot 3.1416 \cdot 10m \cdot 30m \cdot (\frac{180°}{2 \cdot 3.1416}))}{2})) \cdot (\frac{180°}{2 \cdot 3.1416})

Next Step Convert Units

∴

V Sector = (2 \cdot 3.1416 \cdot 10m \cdot (\frac{1050m² - (2 \cdot 3.1416 \cdot 10m \cdot 30m \cdot (\frac{3.1416rad}{2 \cdot 3.1416}))}{2})) \cdot (\frac{3.1416rad}{2 \cdot 3.1416})

Next Step Prepare to Evaluate

∴

V Sector = (2 \cdot 3.1416 \cdot 10 \cdot (\frac{1050 - (2 \cdot 3.1416 \cdot 10 \cdot 30 \cdot (\frac{3.1416}{2 \cdot 3.1416}))}{2})) \cdot (\frac{3.1416}{2 \cdot 3.1416})

Next Step Evaluate

∴

V Sector = 1688.95482971485m³

LAST Step Rounding Answer

∴

V Sector = 1688.9548m³

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

Formulas to find Volume of Toroid Sector

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.

Formulas to find Radius of Toroid

Total Surface Area of Toroid Sector

Total Surface Area of Toroid Sector is the total quantity of two-dimensional space enclosed on the entire surface of the Toroid Sector.

Symbol: TSA_Sector

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Toroid Sector

Cross Sectional Perimeter of Toroid

Cross Sectional Perimeter of Toroid is the total length of the boundary of the cross-section of the Toroid.

Symbol: P_{Cross Section}

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Cross Sectional Perimeter of Toroid

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.

Formulas to find Angle of Intersection of Toroid Sector

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

Other Formulas to find Volume of Toroid Sector

Go Volume of Toroid Sector

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

Go Volume of Toroid Sector given Base Area

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

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}))

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

Volume of Toroid Sector given Total Surface Area and Angle of Intersection evaluator uses 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)) to evaluate the Volume of Toroid Sector, Volume of Toroid Sector given Total Surface Area and Angle of Intersection formula is defined as the amount of three-dimensional space occupied by the Toroid sector, calculated using total surface area and angle of intersection of Toroid Sector. Volume of Toroid Sector is denoted by V_Sector symbol.

How to evaluate Volume of Toroid Sector given Total Surface Area and Angle of Intersection using this online evaluator? To use this online evaluator for Volume of Toroid Sector given Total Surface Area and Angle of Intersection, enter Radius of Toroid (r), Total Surface Area of Toroid Sector (TSA_Sector), Cross Sectional Perimeter of Toroid (P_{Cross Section}) & Angle of Intersection of Toroid Sector (∠_Intersection) and hit the calculate button.

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

What is the formula to find Volume of Toroid Sector given Total Surface Area and Angle of Intersection?

The formula of Volume of Toroid Sector given Total Surface Area and Angle of Intersection is expressed as 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)). Here is an example- 1688.955 = (2*pi*10*((1050-(2*pi*10*30*(3.1415926535892/(2*pi))))/2))*(3.1415926535892/(2*pi)).

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

With Radius of Toroid (r), Total Surface Area of Toroid Sector (TSA_Sector), Cross Sectional Perimeter of Toroid (P_{Cross Section}) & Angle of Intersection of Toroid Sector (∠_Intersection) we can find Volume of Toroid Sector given Total Surface Area and Angle of Intersection using the formula - 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)). 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*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*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 given Total Surface Area and Angle of Intersection be negative?

No, the Volume of Toroid Sector given Total Surface Area and Angle of Intersection, measured in Volume cannot be negative.

Which unit is used to measure Volume of Toroid Sector given Total Surface Area and Angle of Intersection?

Volume of Toroid Sector given Total Surface Area and Angle of Intersection 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 given Total Surface Area and Angle of Intersection can be measured.

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

​GoVolume of Toroid Sector Formula

​GoVolume of Toroid Sector given Base Area Formula

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

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

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

Other Formulas to find Volume of Toroid Sector

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

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

Variable Name

GoVolume of Toroid Sector Formula

GoVolume of Toroid Sector given Base Area Formula