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Radius of Toroid given Total Surface Area of Toroid Sector Formula

GoRadius of Toroid given Volume of Toroid Sector Formula

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Radius of Toroid is the line connecting the center of the overall Toroid to the center of a cross-section of the Toroid. Check FAQs

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

r - Radius of Toroid?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?

Radius of Toroid given Total Surface Area of Toroid Sector Example

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

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

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

10.0798 = \frac{1050 - (2 \cdot 50)}{2 \cdot 3.1416 \cdot 30 \cdot (\frac{180}{2 \cdot 3.1416})}

10.0798m = \frac{1050m² - (2 \cdot 50m²)}{2 \cdot 3.1416 \cdot 30m \cdot (\frac{180°}{2 \cdot 3.1416})}

10.0798 = \frac{1050 - (2 \cdot 50)}{2 \cdot 3.1416 \cdot 30 \cdot (\frac{180}{2 \cdot 3.1416})}

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Radius of Toroid given Total Surface Area of Toroid Sector Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Substitute values of Constants

∴

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

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

r = 10.0798130624886m

LAST Step Rounding Answer

∴

r = 10.0798m

Radius of Toroid given Total Surface Area of Toroid Sector Formula Elements

Variables

Constants

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

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 Radius of Toroid

Go Radius of Toroid given Volume of Toroid Sector

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

Other formulas in Toroid Sector category

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})})

Go Cross Sectional Perimeter of Toroid given Total Surface Area of Toroid Sector

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

How to Evaluate Radius of Toroid given Total Surface Area of Toroid Sector?

Radius of Toroid given Total Surface Area of Toroid Sector evaluator uses Radius of Toroid = (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))) to evaluate the Radius of Toroid, The Radius of Toroid given Total Surface Area of Toroid Sector formula is defined as the line connecting the center of overall Toroid to the center of cross section of Toroid, calculated using total surface area of Toroid Sector. Radius of Toroid is denoted by r symbol.

How to evaluate Radius of Toroid given Total Surface Area of Toroid Sector using this online evaluator? To use this online evaluator for Radius of Toroid given Total Surface Area of Toroid Sector, 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 Radius of Toroid given Total Surface Area of Toroid Sector

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

The formula of Radius of Toroid given Total Surface Area of Toroid Sector is expressed as Radius of Toroid = (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))). Here is an example- 10.07981 = (1050-(2*50))/(2*pi*30*(3.1415926535892/(2*pi))).

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

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 Radius of Toroid given Total Surface Area of Toroid Sector using the formula - Radius of Toroid = (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))). This formula also uses Archimedes' constant .

What are the other ways to Calculate Radius of Toroid?

Here are the different ways to Calculate Radius of Toroid-

Radius of Toroid=(Volume of Toroid Sector/(2*pi*Cross Sectional Area of Toroid*(Angle of Intersection of Toroid Sector/(2*pi))))

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

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

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

Radius of Toroid given Total Surface Area of Toroid Sector is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Radius of Toroid given Total Surface Area of Toroid Sector can be measured.

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Radius of Toroid given Total Surface Area of Toroid Sector Formula

​GoRadius of Toroid given Volume of Toroid Sector Formula

Radius of Toroid given Total Surface Area of Toroid Sector Example

Radius of Toroid given Total Surface Area of Toroid Sector Solution

Radius of Toroid given Total Surface Area of Toroid Sector Formula Elements

Other Formulas to find Radius of Toroid

Other formulas in Toroid Sector category

How to Evaluate Radius of Toroid given Total Surface Area of Toroid Sector?

FAQs on Radius of Toroid given Total Surface Area of Toroid Sector

Variable Name

GoRadius of Toroid given Volume of Toroid Sector Formula