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Volume of Toroid Sector given Total Surface Area Formula

GoVolume of Toroid Sector 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 A Cross Section) \cdot ((\frac{TSA Sector - (2 \cdot A Cross Section)}{2 \cdot π \cdot P Cross Section}))

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

Volume of Toroid Sector given Total Surface Area Example

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

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

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

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

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

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

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Home » Math » Geometry » 3D Geometry » Volume of Toroid Sector given Total Surface Area

Volume of Toroid Sector given Total Surface Area Solution

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

FIRST Step Consider the formula

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}))

Next Step Substitute values of Variables

∴

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

Next Step Substitute values of Constants

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

V Sector = 1583.33333333333m³

LAST Step Rounding Answer

∴

V Sector = 1583.3333m³

Volume of Toroid Sector given Total Surface 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.

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.

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.

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.

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

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

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 given Total Surface Area?

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

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

FAQs on Volume of Toroid Sector given Total Surface Area

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

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

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

With Cross Sectional Area of Toroid (A_{Cross Section}), Total Surface Area of Toroid Sector (TSA_Sector) & Cross Sectional Perimeter of Toroid (P_{Cross Section}) we can find Volume of Toroid Sector given Total Surface Area using the formula - 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))). 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))

Can the Volume of Toroid Sector given Total Surface Area be negative?

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

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

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