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Total Surface Area of Toroid Sector given Volume and Angle of Intersection Formula

GoTotal Surface Area of Toroid Sector Formula

GoTotal Surface Area of Toroid Sector given Volume of Toroid Sector Formula

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Total Surface Area of Toroid Sector is the total quantity of two-dimensional space enclosed on the entire surface of the Toroid Sector. Check FAQs

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

TSA_Sector - Total Surface Area of Toroid Sector?r - Radius of Toroid?P_{Cross Section} - Cross Sectional Perimeter of Toroid?∠_Intersection - Angle of Intersection of Toroid Sector?V_Sector - Volume of Toroid Sector?π - Archimedes' constant?

Total Surface Area of Toroid Sector given Volume and Angle of Intersection Example

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

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

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

1042.4271 = ((2 \cdot 3.1416 \cdot 10 \cdot 30) \cdot (\frac{180}{2 \cdot 3.1416})) + (2 \cdot (\frac{1570}{2 \cdot 3.1416 \cdot 10 \cdot (\frac{180}{2 \cdot 3.1416})}))

1042.4271m² = ((2 \cdot 3.1416 \cdot 10m \cdot 30m) \cdot (\frac{180°}{2 \cdot 3.1416})) + (2 \cdot (\frac{1570m³}{2 \cdot 3.1416 \cdot 10m \cdot (\frac{180°}{2 \cdot 3.1416})}))

1042.4271 = ((2 \cdot 3.1416 \cdot 10 \cdot 30) \cdot (\frac{180}{2 \cdot 3.1416})) + (2 \cdot (\frac{1570}{2 \cdot 3.1416 \cdot 10 \cdot (\frac{180}{2 \cdot 3.1416})}))

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Total Surface Area of Toroid Sector given Volume and Angle of Intersection Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

TSA Sector = ((2 \cdot π \cdot 10m \cdot 30m) \cdot (\frac{180°}{2 \cdot π})) + (2 \cdot (\frac{1570m³}{2 \cdot π \cdot 10m \cdot (\frac{180°}{2 \cdot π})}))

Next Step Substitute values of Constants

∴

TSA Sector = ((2 \cdot 3.1416 \cdot 10m \cdot 30m) \cdot (\frac{180°}{2 \cdot 3.1416})) + (2 \cdot (\frac{1570m³}{2 \cdot 3.1416 \cdot 10m \cdot (\frac{180°}{2 \cdot 3.1416})}))

Next Step Convert Units

∴

TSA Sector = ((2 \cdot 3.1416 \cdot 10m \cdot 30m) \cdot (\frac{3.1416rad}{2 \cdot 3.1416})) + (2 \cdot (\frac{1570m³}{2 \cdot 3.1416 \cdot 10m \cdot (\frac{3.1416rad}{2 \cdot 3.1416})}))

Next Step Prepare to Evaluate

∴

TSA Sector = ((2 \cdot 3.1416 \cdot 10 \cdot 30) \cdot (\frac{3.1416}{2 \cdot 3.1416})) + (2 \cdot (\frac{1570}{2 \cdot 3.1416 \cdot 10 \cdot (\frac{3.1416}{2 \cdot 3.1416})}))

Next Step Evaluate

∴

TSA Sector = 1042.42710033849m²

LAST Step Rounding Answer

∴

TSA Sector = 1042.4271m²

Total Surface Area of Toroid Sector given Volume and Angle of Intersection Formula Elements

Variables

Constants

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.

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.

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.

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.

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.

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 Total Surface Area of Toroid Sector

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 of Toroid Sector

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

How to Evaluate Total Surface Area of Toroid Sector given Volume and Angle of Intersection?

Total Surface Area of Toroid Sector given Volume and Angle of Intersection evaluator uses 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*(Volume of Toroid Sector/(2*pi*Radius of Toroid*(Angle of Intersection of Toroid Sector/(2*pi))))) to evaluate the Total Surface Area of Toroid Sector, Total Surface Area of Toroid Sector given Volume and Angle of Intersection formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Toroid Sector, calculated using volume and angle of intersection of Toroid Sector. Total Surface Area of Toroid Sector is denoted by TSA_Sector symbol.

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

FAQs on Total Surface Area of Toroid Sector given Volume and Angle of Intersection

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

The formula of Total Surface Area of Toroid Sector given Volume and Angle of Intersection is expressed as 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*(Volume of Toroid Sector/(2*pi*Radius of Toroid*(Angle of Intersection of Toroid Sector/(2*pi))))). Here is an example- 1042.427 = ((2*pi*10*30)*(3.1415926535892/(2*pi)))+(2*(1570/(2*pi*10*(3.1415926535892/(2*pi))))).

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

With Radius of Toroid (r), Cross Sectional Perimeter of Toroid (P_{Cross Section}), Angle of Intersection of Toroid Sector (∠_Intersection) & Volume of Toroid Sector (V_Sector) we can find Total Surface Area of Toroid Sector given Volume and Angle of Intersection using the formula - 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*(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 Total Surface Area of Toroid Sector?

Here are the different ways to Calculate Total Surface Area of Toroid Sector-

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*Cross Sectional Area of Toroid)
Total Surface Area of Toroid Sector=((2*pi*(Volume of Toroid Sector/(2*pi*Cross Sectional Area of Toroid*(Angle of Intersection of Toroid Sector/(2*pi))))*Cross Sectional Perimeter of Toroid)*(Angle of Intersection of Toroid Sector/(2*pi)))+(2*Cross Sectional Area of Toroid)
Total Surface Area of Toroid Sector=((2*pi*Cross Sectional Perimeter of Toroid)*((Volume of Toroid Sector/(2*pi*Cross Sectional Area of Toroid))))+(2*Cross Sectional Area of Toroid)

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

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

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

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

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Total Surface Area of Toroid Sector given Volume and Angle of Intersection Formula

​GoTotal Surface Area of Toroid Sector Formula

​GoTotal Surface Area of Toroid Sector given Volume of Toroid Sector Formula

Total Surface Area of Toroid Sector given Volume and Angle of Intersection Example

Total Surface Area of Toroid Sector given Volume and Angle of Intersection Solution

Total Surface Area of Toroid Sector given Volume and Angle of Intersection Formula Elements

Credits

Other Formulas to find Total Surface Area of Toroid Sector

How to Evaluate Total Surface Area of Toroid Sector given Volume and Angle of Intersection?

FAQs on Total Surface Area of Toroid Sector given Volume and Angle of Intersection

Variable Name

GoTotal Surface Area of Toroid Sector Formula

GoTotal Surface Area of Toroid Sector given Volume of Toroid Sector Formula