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Volume of Torus Sector given Minor Radius, Lateral Surface Area, and Angle of Intersection Formula

GoVolume of Torus Sector Formula

GoVolume of Torus Sector given Lateral 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 (\frac{LSA Sector}{4 \cdot (π^{2}) \cdot (r Circular Section) \cdot (\frac{∠ Intersection}{2 \cdot π})}) \cdot ({r Circular Section}^{2}) \cdot (\frac{∠ Intersection}{2 \cdot π}))

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

Volume of Torus Sector given Minor Radius, Lateral Surface Area, and Angle of Intersection Example

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Here is how the Volume of Torus Sector given Minor Radius, Lateral Surface Area, and Angle of Intersection equation looks like with Values.

Here is how the Volume of Torus Sector given Minor Radius, Lateral Surface Area, and Angle of Intersection equation looks like with Units.

Here is how the Volume of Torus Sector given Minor Radius, Lateral Surface Area, and Angle of Intersection equation looks like.

1040 = (2 \cdot ({3.1416}^{2}) \cdot (\frac{260}{4 \cdot ({3.1416}^{2}) \cdot (8) \cdot (\frac{30}{2 \cdot 3.1416})}) \cdot (8^{2}) \cdot (\frac{30}{2 \cdot 3.1416}))

1040m³ = (2 \cdot ({3.1416}^{2}) \cdot (\frac{260m²}{4 \cdot ({3.1416}^{2}) \cdot (8m) \cdot (\frac{30°}{2 \cdot 3.1416})}) \cdot ({8m}^{2}) \cdot (\frac{30°}{2 \cdot 3.1416}))

1040 = (2 \cdot ({3.1416}^{2}) \cdot (\frac{260}{4 \cdot ({3.1416}^{2}) \cdot (8) \cdot (\frac{30}{2 \cdot 3.1416})}) \cdot (8^{2}) \cdot (\frac{30}{2 \cdot 3.1416}))

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Volume of Torus Sector given Minor Radius, Lateral Surface Area, and Angle of Intersection Solution

Follow our step by step solution on how to calculate Volume of Torus Sector given Minor Radius, Lateral Surface Area, and Angle of Intersection?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

V Sector = (2 \cdot (π^{2}) \cdot (\frac{260m²}{4 \cdot (π^{2}) \cdot (8m) \cdot (\frac{30°}{2 \cdot π})}) \cdot ({8m}^{2}) \cdot (\frac{30°}{2 \cdot π}))

Next Step Substitute values of Constants

∴

V Sector = (2 \cdot ({3.1416}^{2}) \cdot (\frac{260m²}{4 \cdot ({3.1416}^{2}) \cdot (8m) \cdot (\frac{30°}{2 \cdot 3.1416})}) \cdot ({8m}^{2}) \cdot (\frac{30°}{2 \cdot 3.1416}))

Next Step Convert Units

∴

V Sector = (2 \cdot ({3.1416}^{2}) \cdot (\frac{260m²}{4 \cdot ({3.1416}^{2}) \cdot (8m) \cdot (\frac{0.5236rad}{2 \cdot 3.1416})}) \cdot ({8m}^{2}) \cdot (\frac{0.5236rad}{2 \cdot 3.1416}))

Next Step Prepare to Evaluate

∴

V Sector = (2 \cdot ({3.1416}^{2}) \cdot (\frac{260}{4 \cdot ({3.1416}^{2}) \cdot (8) \cdot (\frac{0.5236}{2 \cdot 3.1416})}) \cdot (8^{2}) \cdot (\frac{0.5236}{2 \cdot 3.1416}))

LAST Step Evaluate

∴

V Sector = 1040m³

Volume of Torus Sector given Minor Radius, Lateral Surface Area, and Angle of Intersection 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

Lateral Surface Area of Torus Sector

Lateral Surface Area of Torus Sector is the total quantity of two-dimensional plane enclosed on the lateral curved surface of the Torus Sector.

Symbol: LSA_Sector

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Lateral Surface Area of Torus Sector

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

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

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 Radius

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

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}))

How to Evaluate Volume of Torus Sector given Minor Radius, Lateral Surface Area, and Angle of Intersection?

Volume of Torus Sector given Minor Radius, Lateral Surface Area, and Angle of Intersection evaluator uses Volume of Torus Sector = (2*(pi^2)*(Lateral Surface Area of Torus Sector/(4*(pi^2)*(Radius of Circular Section of Torus)*(Angle of Intersection of Torus Sector/(2*pi))))*(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 given Minor Radius, Lateral Surface Area, and Angle of Intersection formula is defined as the amount of three-dimensional space covered by the Torus Sector, calculated using minor radius, lateral surface area, and angle of intersection. Volume of Torus Sector is denoted by V_Sector symbol.

How to evaluate Volume of Torus Sector given Minor Radius, Lateral Surface Area, and Angle of Intersection using this online evaluator? To use this online evaluator for Volume of Torus Sector given Minor Radius, Lateral Surface Area, and Angle of Intersection, enter Lateral Surface Area of Torus Sector (LSA_Sector), 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 given Minor Radius, Lateral Surface Area, and Angle of Intersection

What is the formula to find Volume of Torus Sector given Minor Radius, Lateral Surface Area, and Angle of Intersection?

The formula of Volume of Torus Sector given Minor Radius, Lateral Surface Area, and Angle of Intersection is expressed as Volume of Torus Sector = (2*(pi^2)*(Lateral Surface Area of Torus Sector/(4*(pi^2)*(Radius of Circular Section of Torus)*(Angle of Intersection of Torus Sector/(2*pi))))*(Radius of Circular Section of Torus^2)*(Angle of Intersection of Torus Sector/(2*pi))). Here is an example- 1040 = (2*(pi^2)*(260/(4*(pi^2)*(8)*(0.5235987755982/(2*pi))))*(8^2)*(0.5235987755982/(2*pi))).

How to calculate Volume of Torus Sector given Minor Radius, Lateral Surface Area, and Angle of Intersection?

With Lateral Surface Area of Torus Sector (LSA_Sector), Radius of Circular Section of Torus (r_{Circular Section}) & Angle of Intersection of Torus Sector (∠_Intersection) we can find Volume of Torus Sector given Minor Radius, Lateral Surface Area, and Angle of Intersection using the formula - Volume of Torus Sector = (2*(pi^2)*(Lateral Surface Area of Torus Sector/(4*(pi^2)*(Radius of Circular Section of Torus)*(Angle of Intersection of Torus Sector/(2*pi))))*(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=(2*(pi^2)*(Radius of Torus)*(Radius of Circular Section of Torus^2)*(Angle of Intersection of Torus Sector/(2*pi)))
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)*((Lateral Surface Area of Torus Sector/(4*(pi^2)*(Radius of Torus)*(Angle of Intersection of Torus Sector/(2*pi))))^2)*(Angle of Intersection of Torus Sector/(2*pi)))

Can the Volume of Torus Sector given Minor Radius, Lateral Surface Area, and Angle of Intersection be negative?

No, the Volume of Torus Sector given Minor Radius, Lateral Surface Area, and Angle of Intersection, measured in Volume cannot be negative.

Which unit is used to measure Volume of Torus Sector given Minor Radius, Lateral Surface Area, and Angle of Intersection?

Volume of Torus Sector given Minor Radius, Lateral 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 Torus Sector given Minor Radius, Lateral Surface Area, and Angle of Intersection can be measured.

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Volume of Torus Sector given Minor Radius, Lateral Surface Area, and Angle of Intersection Formula

​GoVolume of Torus Sector Formula

​GoVolume of Torus Sector given Lateral Surface Area Formula

Volume of Torus Sector given Minor Radius, Lateral Surface Area, and Angle of Intersection Example

Volume of Torus Sector given Minor Radius, Lateral Surface Area, and Angle of Intersection Solution

Volume of Torus Sector given Minor Radius, Lateral Surface Area, and Angle of Intersection Formula Elements

Other Formulas to find Volume of Torus Sector

How to Evaluate Volume of Torus Sector given Minor Radius, Lateral Surface Area, and Angle of Intersection?

FAQs on Volume of Torus Sector given Minor Radius, Lateral Surface Area, and Angle of Intersection

Variable Name

GoVolume of Torus Sector Formula

GoVolume of Torus Sector given Lateral Surface Area Formula