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Surface to Volume Ratio of Toroid Sector Formula

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Surface to Volume Ratio of Toroid Sector is the numerical ratio of the total surface area of the Toroid Sector to the volume of the Toroid Sector. Check FAQs

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

R_A/V(Sector) - Surface to Volume Ratio of Toroid Sector?r - Radius of Toroid?P_{Cross Section} - Cross Sectional Perimeter of Toroid?∠_Intersection - Angle of Intersection of Toroid Sector?A_{Cross Section} - Cross Sectional Area of Toroid?π - Archimedes' constant?

Surface to Volume Ratio of Toroid Sector Example

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Here is how the Surface to Volume Ratio of Toroid Sector equation looks like with Values.

Here is how the Surface to Volume Ratio of Toroid Sector equation looks like with Units.

Here is how the Surface to Volume Ratio of Toroid Sector equation looks like.

0.6637 = \frac{(2 \cdot 3.1416 \cdot 10 \cdot 30 \cdot (\frac{180}{2 \cdot 3.1416})) + (2 \cdot 50)}{2 \cdot 3.1416 \cdot 10 \cdot 50 \cdot (\frac{180}{2 \cdot 3.1416})}

0.6637m⁻¹ = \frac{(2 \cdot 3.1416 \cdot 10m \cdot 30m \cdot (\frac{180°}{2 \cdot 3.1416})) + (2 \cdot 50m²)}{2 \cdot 3.1416 \cdot 10m \cdot 50m² \cdot (\frac{180°}{2 \cdot 3.1416})}

0.6637 = \frac{(2 \cdot 3.1416 \cdot 10 \cdot 30 \cdot (\frac{180}{2 \cdot 3.1416})) + (2 \cdot 50)}{2 \cdot 3.1416 \cdot 10 \cdot 50 \cdot (\frac{180}{2 \cdot 3.1416})}

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Surface to Volume Ratio of Toroid Sector Solution

Follow our step by step solution on how to calculate Surface to Volume Ratio of Toroid Sector?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

R A/V(Sector) = \frac{(2 \cdot π \cdot 10m \cdot 30m \cdot (\frac{180°}{2 \cdot π})) + (2 \cdot 50m²)}{2 \cdot π \cdot 10m \cdot 50m² \cdot (\frac{180°}{2 \cdot π})}

Next Step Substitute values of Constants

∴

R A/V(Sector) = \frac{(2 \cdot 3.1416 \cdot 10m \cdot 30m \cdot (\frac{180°}{2 \cdot 3.1416})) + (2 \cdot 50m²)}{2 \cdot 3.1416 \cdot 10m \cdot 50m² \cdot (\frac{180°}{2 \cdot 3.1416})}

Next Step Convert Units

∴

R A/V(Sector) = \frac{(2 \cdot 3.1416 \cdot 10m \cdot 30m \cdot (\frac{3.1416rad}{2 \cdot 3.1416})) + (2 \cdot 50m²)}{2 \cdot 3.1416 \cdot 10m \cdot 50m² \cdot (\frac{3.1416rad}{2 \cdot 3.1416})}

Next Step Prepare to Evaluate

∴

R A/V(Sector) = \frac{(2 \cdot 3.1416 \cdot 10 \cdot 30 \cdot (\frac{3.1416}{2 \cdot 3.1416})) + (2 \cdot 50)}{2 \cdot 3.1416 \cdot 10 \cdot 50 \cdot (\frac{3.1416}{2 \cdot 3.1416})}

Next Step Evaluate

∴

R A/V(Sector) = 0.66366197723677m⁻¹

LAST Step Rounding Answer

∴

R A/V(Sector) = 0.6637m⁻¹

Surface to Volume Ratio of Toroid Sector Formula Elements

Variables

Constants

Surface to Volume Ratio of Toroid Sector

Surface to Volume Ratio of Toroid Sector is the numerical ratio of the total surface area of the Toroid Sector to the volume of the Toroid Sector.

Symbol: R_A/V(Sector)

Measurement: Reciprocal LengthUnit: m⁻¹

Note: Value should be greater than 0.

Formulas to find Surface to Volume Ratio 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

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

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

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 in Surface to Volume Ratio category

Go Surface to Volume Ratio of Toroid

R A/V = (\frac{P Cross Section}{A Cross Section})

Go Surface to Volume Ratio of Toroid given Total Surface Area

R A/V = (\frac{TSA}{2 \cdot π \cdot r \cdot A Cross Section})

How to Evaluate Surface to Volume Ratio of Toroid Sector?

Surface to Volume Ratio of Toroid Sector evaluator uses Surface to Volume Ratio 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))/(2*pi*Radius of Toroid*Cross Sectional Area of Toroid*(Angle of Intersection of Toroid Sector/(2*pi))) to evaluate the Surface to Volume Ratio of Toroid Sector, Surface to Volume Ratio of Toroid Sector formula is defined as the numerical ratio of the total surface area of the Toroid Sector to the volume of the Toroid Sector. Surface to Volume Ratio of Toroid Sector is denoted by R_A/V(Sector) symbol.

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

FAQs on Surface to Volume Ratio of Toroid Sector

What is the formula to find Surface to Volume Ratio of Toroid Sector?

The formula of Surface to Volume Ratio of Toroid Sector is expressed as Surface to Volume Ratio 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))/(2*pi*Radius of Toroid*Cross Sectional Area of Toroid*(Angle of Intersection of Toroid Sector/(2*pi))). Here is an example- 0.663662 = ((2*pi*10*30*(3.1415926535892/(2*pi)))+(2*50))/(2*pi*10*50*(3.1415926535892/(2*pi))).

How to calculate Surface to Volume Ratio of Toroid Sector?

With Radius of Toroid (r), Cross Sectional Perimeter of Toroid (P_{Cross Section}), Angle of Intersection of Toroid Sector (∠_Intersection) & Cross Sectional Area of Toroid (A_{Cross Section}) we can find Surface to Volume Ratio of Toroid Sector using the formula - Surface to Volume Ratio 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))/(2*pi*Radius of Toroid*Cross Sectional Area of Toroid*(Angle of Intersection of Toroid Sector/(2*pi))). This formula also uses Archimedes' constant .

Can the Surface to Volume Ratio of Toroid Sector be negative?

No, the Surface to Volume Ratio of Toroid Sector, measured in Reciprocal Length cannot be negative.

Which unit is used to measure Surface to Volume Ratio of Toroid Sector?

Surface to Volume Ratio of Toroid Sector is usually measured using the 1 per Meter[m⁻¹] for Reciprocal Length. 1 per Kilometer[m⁻¹], 1 per Mile[m⁻¹], 1 per Yard[m⁻¹] are the few other units in which Surface to Volume Ratio of Toroid Sector can be measured.

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Surface to Volume Ratio of Toroid Sector Formula

Surface to Volume Ratio of Toroid Sector Example

Surface to Volume Ratio of Toroid Sector Solution

Surface to Volume Ratio of Toroid Sector Formula Elements

Other formulas in Surface to Volume Ratio category

How to Evaluate Surface to Volume Ratio of Toroid Sector?

FAQs on Surface to Volume Ratio of Toroid Sector

Variable Name