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Volume of Torus Sector Formula

GoVolume of Torus Sector given Lateral Surface Area Formula

GoVolume of Torus Sector given Lateral Surface Area and Total Surface Area Formula

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

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

V_Sector - Volume of Torus Sector?r - Radius of Torus?r_{Circular Section} - Radius of Circular Section of Torus?∠_Intersection - Angle of Intersection of Torus Sector?π - Archimedes' constant?

Volume of Torus Sector Example

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

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

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

1052.7578 = (2 \cdot ({3.1416}^{2}) \cdot (10) \cdot (8^{2}) \cdot (\frac{30}{2 \cdot 3.1416}))

1052.7578m³ = (2 \cdot ({3.1416}^{2}) \cdot (10m) \cdot ({8m}^{2}) \cdot (\frac{30°}{2 \cdot 3.1416}))

1052.7578 = (2 \cdot ({3.1416}^{2}) \cdot (10) \cdot (8^{2}) \cdot (\frac{30}{2 \cdot 3.1416}))

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Volume of Torus Sector Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

V Sector = (2 \cdot (π^{2}) \cdot (10m) \cdot ({8m}^{2}) \cdot (\frac{30°}{2 \cdot π}))

Next Step Substitute values of Constants

∴

V Sector = (2 \cdot ({3.1416}^{2}) \cdot (10m) \cdot ({8m}^{2}) \cdot (\frac{30°}{2 \cdot 3.1416}))

Next Step Convert Units

∴

V Sector = (2 \cdot ({3.1416}^{2}) \cdot (10m) \cdot ({8m}^{2}) \cdot (\frac{0.5236rad}{2 \cdot 3.1416}))

Next Step Prepare to Evaluate

∴

V Sector = (2 \cdot ({3.1416}^{2}) \cdot (10) \cdot (8^{2}) \cdot (\frac{0.5236}{2 \cdot 3.1416}))

Next Step Evaluate

∴

V Sector = 1052.75780278267m³

LAST Step Rounding Answer

∴

V Sector = 1052.7578m³

Volume of Torus Sector Formula Elements

Variables

Constants

Volume of Torus Sector

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

Symbol: V_Sector

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Torus Sector

Radius of Torus

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

Symbol: r

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Torus

Radius of Circular Section of Torus

Radius of Circular Section of Torus is the line connecting the center of the circular cross section to any point on the circumference of the circular cross section of the Torus.

Symbol: r_{Circular Section}

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Circular Section of Torus

Angle of Intersection of Torus Sector

Angle of Intersection of Torus Sector is the angle subtended by the planes in which each of the circular end faces of the Torus Sector is contained.

Symbol: ∠_Intersection

Measurement: AngleUnit: °

Note: Value should be between 0 to 360.

Formulas to find Angle of Intersection of Torus 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 Torus Sector

Go Volume of Torus Sector given Lateral Surface Area

V Sector = \frac{r Circular Section \cdot LSA Sector}{2}

Go Volume of Torus Sector given Lateral Surface Area and Total Surface Area

V Sector = (2 \cdot (π^{2}) \cdot (r) \cdot (\frac{TSA Sector - LSA Sector}{2 \cdot π}) \cdot (\frac{∠ Intersection}{2 \cdot π}))

Other formulas in Volume of Torus Sector category

Go Lateral Surface Area of Torus Sector

LSA Sector = (4 \cdot (π^{2}) \cdot (r) \cdot (r Circular Section) \cdot (\frac{∠ Intersection}{2 \cdot π}))

Go Lateral Surface Area of Torus Sector given Volume

LSA Sector = 2 \cdot (\frac{V Sector}{r Circular Section})

Go Total Surface Area of Torus Sector

TSA Sector = (LSA Sector + (2 \cdot π \cdot ({r Circular Section}^{2})))

Go Total Surface Area of Torus Sector given Lateral Surface Area and Radius

TSA Sector = (LSA Sector + (2 \cdot π \cdot ({(\frac{LSA Sector}{4 \cdot (π^{2}) \cdot (r) \cdot (\frac{∠ Intersection}{2 \cdot π})})}^{2})))

How to Evaluate Volume of Torus Sector?

Volume of Torus Sector evaluator uses Volume of Torus Sector = (2*(pi^2)*(Radius of Torus)*(Radius of Circular Section of Torus^2)*(Angle of Intersection of Torus Sector/(2*pi))) to evaluate the Volume of Torus Sector, Volume of Torus Sector formula is defined as amount of three dimensional space covered by Torus Sector. Volume of Torus Sector is denoted by V_Sector symbol.

How to evaluate Volume of Torus Sector using this online evaluator? To use this online evaluator for Volume of Torus Sector, enter Radius of Torus (r), Radius of Circular Section of Torus (r_{Circular Section}) & Angle of Intersection of Torus Sector (∠_Intersection) and hit the calculate button.

FAQs on Volume of Torus Sector

What is the formula to find Volume of Torus Sector?

The formula of Volume of Torus Sector is expressed as Volume of Torus Sector = (2*(pi^2)*(Radius of Torus)*(Radius of Circular Section of Torus^2)*(Angle of Intersection of Torus Sector/(2*pi))). Here is an example- 1052.758 = (2*(pi^2)*(10)*(8^2)*(0.5235987755982/(2*pi))).

How to calculate Volume of Torus Sector?

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

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

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

Volume of Torus Sector=(Radius of Circular Section of Torus*Lateral Surface Area of Torus Sector)/2
Volume of Torus Sector=(2*(pi^2)*(Radius of Torus)*((Total Surface Area of Torus Sector-Lateral Surface Area of Torus Sector)/(2*pi))*(Angle of Intersection of Torus Sector/(2*pi)))

Can the Volume of Torus Sector be negative?

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

Which unit is used to measure Volume of Torus Sector?

Volume of Torus 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 Torus Sector can be measured.

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Volume of Torus Sector Formula

​GoVolume of Torus Sector given Lateral Surface Area Formula

​GoVolume of Torus Sector given Lateral Surface Area and Total Surface Area Formula

Volume of Torus Sector Example

Volume of Torus Sector Solution

Volume of Torus Sector Formula Elements

Other Formulas to find Volume of Torus Sector

Other formulas in Volume of Torus Sector category

How to Evaluate Volume of Torus Sector?

FAQs on Volume of Torus Sector

Variable Name

GoVolume of Torus Sector given Lateral Surface Area Formula

GoVolume of Torus Sector given Lateral Surface Area and Total Surface Area Formula