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Volume of Toroid Sector given Base Area Formula

GoVolume 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 (\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})

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

Volume of Toroid Sector given Base Area Example

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

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

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

1583.3333 = (2 \cdot 3.1416 \cdot (\frac{1050 - (2 \cdot 50)}{2 \cdot 3.1416 \cdot 30 \cdot (\frac{180}{2 \cdot 3.1416})}) \cdot 50) \cdot (\frac{180}{2 \cdot 3.1416})

1583.3333m³ = (2 \cdot 3.1416 \cdot (\frac{1050m² - (2 \cdot 50m²)}{2 \cdot 3.1416 \cdot 30m \cdot (\frac{180°}{2 \cdot 3.1416})}) \cdot 50m²) \cdot (\frac{180°}{2 \cdot 3.1416})

1583.3333 = (2 \cdot 3.1416 \cdot (\frac{1050 - (2 \cdot 50)}{2 \cdot 3.1416 \cdot 30 \cdot (\frac{180}{2 \cdot 3.1416})}) \cdot 50) \cdot (\frac{180}{2 \cdot 3.1416})

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Volume of Toroid Sector given Base Area Solution

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

FIRST Step Consider the formula

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})

Next Step Substitute values of Variables

∴

V Sector = (2 \cdot π \cdot (\frac{1050m² - (2 \cdot 50m²)}{2 \cdot π \cdot 30m \cdot (\frac{180°}{2 \cdot π})}) \cdot 50m²) \cdot (\frac{180°}{2 \cdot π})

Next Step Substitute values of Constants

∴

V Sector = (2 \cdot 3.1416 \cdot (\frac{1050m² - (2 \cdot 50m²)}{2 \cdot 3.1416 \cdot 30m \cdot (\frac{180°}{2 \cdot 3.1416})}) \cdot 50m²) \cdot (\frac{180°}{2 \cdot 3.1416})

Next Step Convert Units

∴

V Sector = (2 \cdot 3.1416 \cdot (\frac{1050m² - (2 \cdot 50m²)}{2 \cdot 3.1416 \cdot 30m \cdot (\frac{3.1416rad}{2 \cdot 3.1416})}) \cdot 50m²) \cdot (\frac{3.1416rad}{2 \cdot 3.1416})

Next Step Prepare to Evaluate

∴

V Sector = (2 \cdot 3.1416 \cdot (\frac{1050 - (2 \cdot 50)}{2 \cdot 3.1416 \cdot 30 \cdot (\frac{3.1416}{2 \cdot 3.1416})}) \cdot 50) \cdot (\frac{3.1416}{2 \cdot 3.1416})

Next Step Evaluate

∴

V Sector = 1583.33333333333m³

LAST Step Rounding Answer

∴

V Sector = 1583.3333m³

Volume of Toroid Sector given Base Area 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

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 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.

Formulas to find Cross Sectional Area of Toroid

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 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}))

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

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})

How to Evaluate Volume of Toroid Sector given Base Area?

Volume of Toroid Sector given Base Area evaluator 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 evaluate 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 evaluate Volume of Toroid Sector given Base Area using this online evaluator? To use this online evaluator 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.

FAQs on Volume of Toroid Sector given Base Area

What is the formula to find Volume of Toroid Sector given Base Area?

The formula of Volume of Toroid Sector given Base Area is expressed as 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)). Here is an example- 1583.333 = (2*pi*((1050-(2*50))/(2*pi*30*(3.1415926535892/(2*pi))))*50)*(3.1415926535892/(2*pi)).

How to calculate Volume of Toroid Sector given Base Area?

With 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) we can find Volume of Toroid Sector given Base Area using the formula - 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)). 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*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))

Can the Volume of Toroid Sector given Base Area be negative?

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

Which unit is used to measure Volume of Toroid Sector given Base Area?

Volume of Toroid Sector given Base Area 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 Base Area can be measured.

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Volume of Toroid Sector given Base Area Formula

​GoVolume of Toroid Sector Formula

​GoVolume of Toroid Sector given Total Surface Area Formula

Volume of Toroid Sector given Base Area Example

Volume of Toroid Sector given Base Area Solution

Volume of Toroid Sector given Base Area Formula Elements

Other Formulas to find Volume of Toroid Sector

How to Evaluate Volume of Toroid Sector given Base Area?

FAQs on Volume of Toroid Sector given Base Area

Variable Name

GoVolume of Toroid Sector Formula

GoVolume of Toroid Sector given Total Surface Area Formula