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Cross Sectional Area of Toroid given Volume of Toroid Sector Formula

GoCross Sectional Area of Toroid given Total Surface Area of Toroid Sector Formula

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Cross Sectional Area of Toroid is the amount of two-dimensional space occupied by the cross-section of the Toroid. Check FAQs

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

A_{Cross Section} - Cross Sectional Area of Toroid?V_Sector - Volume of Toroid Sector?r - Radius of Toroid?∠_Intersection - Angle of Intersection of Toroid Sector?π - Archimedes' constant?

Cross Sectional Area of Toroid given Volume of Toroid Sector Example

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

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

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

49.9747 = (\frac{1570}{2 \cdot 3.1416 \cdot 10 \cdot (\frac{180}{2 \cdot 3.1416})})

49.9747m² = (\frac{1570m³}{2 \cdot 3.1416 \cdot 10m \cdot (\frac{180°}{2 \cdot 3.1416})})

49.9747 = (\frac{1570}{2 \cdot 3.1416 \cdot 10 \cdot (\frac{180}{2 \cdot 3.1416})})

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Cross Sectional Area of Toroid given Volume of Toroid Sector Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

A Cross Section = (\frac{1570m³}{2 \cdot π \cdot 10m \cdot (\frac{180°}{2 \cdot π})})

Next Step Substitute values of Constants

∴

A Cross Section = (\frac{1570m³}{2 \cdot 3.1416 \cdot 10m \cdot (\frac{180°}{2 \cdot 3.1416})})

Next Step Convert Units

∴

A Cross Section = (\frac{1570m³}{2 \cdot 3.1416 \cdot 10m \cdot (\frac{3.1416rad}{2 \cdot 3.1416})})

Next Step Prepare to Evaluate

∴

A Cross Section = (\frac{1570}{2 \cdot 3.1416 \cdot 10 \cdot (\frac{3.1416}{2 \cdot 3.1416})})

Next Step Evaluate

∴

A Cross Section = 49.9746521308646m²

LAST Step Rounding Answer

∴

A Cross Section = 49.9747m²

Cross Sectional Area of Toroid given Volume of Toroid Sector Formula Elements

Variables

Constants

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

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

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 Cross Sectional Area of Toroid

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})

Other formulas in 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 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}))

How to Evaluate Cross Sectional Area of Toroid given Volume of Toroid Sector?

Cross Sectional Area of Toroid given Volume of Toroid Sector evaluator uses Cross Sectional Area of Toroid = (Volume of Toroid Sector/(2*pi*Radius of Toroid*(Angle of Intersection of Toroid Sector/(2*pi)))) to evaluate the Cross Sectional Area of Toroid, Cross Sectional Area of Toroid given Volume of Toroid Sector formula is defined as the amount of two dimensional space occupied by the cross section of Toroid, calculated using volume of the Toroid Sector. Cross Sectional Area of Toroid is denoted by A_{Cross Section} symbol.

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

FAQs on Cross Sectional Area of Toroid given Volume of Toroid Sector

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

The formula of Cross Sectional Area of Toroid given Volume of Toroid Sector is expressed as Cross Sectional Area of Toroid = (Volume of Toroid Sector/(2*pi*Radius of Toroid*(Angle of Intersection of Toroid Sector/(2*pi)))). Here is an example- 49.97465 = (1570/(2*pi*10*(3.1415926535892/(2*pi)))).

How to calculate Cross Sectional Area of Toroid given Volume of Toroid Sector?

With Volume of Toroid Sector (V_Sector), Radius of Toroid (r) & Angle of Intersection of Toroid Sector (∠_Intersection) we can find Cross Sectional Area of Toroid given Volume of Toroid Sector using the formula - Cross Sectional Area of Toroid = (Volume of Toroid Sector/(2*pi*Radius of Toroid*(Angle of Intersection of Toroid Sector/(2*pi)))). This formula also uses Archimedes' constant .

What are the other ways to Calculate Cross Sectional Area of Toroid?

Here are the different ways to Calculate Cross Sectional Area of Toroid-

Cross Sectional Area 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)

Can the Cross Sectional Area of Toroid given Volume of Toroid Sector be negative?

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

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

Cross Sectional Area of Toroid given Volume of Toroid Sector is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Cross Sectional Area of Toroid given Volume of Toroid Sector can be measured.

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Cross Sectional Area of Toroid given Volume of Toroid Sector Formula

​GoCross Sectional Area of Toroid given Total Surface Area of Toroid Sector Formula

Cross Sectional Area of Toroid given Volume of Toroid Sector Example

Cross Sectional Area of Toroid given Volume of Toroid Sector Solution

Cross Sectional Area of Toroid given Volume of Toroid Sector Formula Elements

Other Formulas to find Cross Sectional Area of Toroid

Other formulas in Toroid Sector category

How to Evaluate Cross Sectional Area of Toroid given Volume of Toroid Sector?

FAQs on Cross Sectional Area of Toroid given Volume of Toroid Sector

Variable Name

GoCross Sectional Area of Toroid given Total Surface Area of Toroid Sector Formula