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Radius of Circular Section of Torus given Volume of Torus Sector Formula

GoRadius of Circular Section of Torus given Lateral Surface Area of Torus Sector Formula

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Radius of Circular Section of Torus is the line connecting the center of the circular cross section to any point on the circumference of the circular cross section of the Torus. Check FAQs

r Circular Section = \sqrt{\frac{V Sector}{2 \cdot (π^{2}) \cdot (r) \cdot (\frac{∠ Intersection}{2 \cdot π})}}

r_{Circular Section} - Radius of Circular Section of Torus?V_Sector - Volume of Torus Sector?r - Radius of Torus?∠_Intersection - Angle of Intersection of Torus Sector?π - Archimedes' constant?

Radius of Circular Section of Torus given Volume of Torus Sector Example

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Here is how the Radius of Circular Section of Torus given Volume of Torus Sector equation looks like with Values.

Here is how the Radius of Circular Section of Torus given Volume of Torus Sector equation looks like with Units.

Here is how the Radius of Circular Section of Torus given Volume of Torus Sector equation looks like.

7.9895 = \sqrt{\frac{1050}{2 \cdot ({3.1416}^{2}) \cdot (10) \cdot (\frac{30}{2 \cdot 3.1416})}}

7.9895m = \sqrt{\frac{1050m³}{2 \cdot ({3.1416}^{2}) \cdot (10m) \cdot (\frac{30°}{2 \cdot 3.1416})}}

7.9895 = \sqrt{\frac{1050}{2 \cdot ({3.1416}^{2}) \cdot (10) \cdot (\frac{30}{2 \cdot 3.1416})}}

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Radius of Circular Section of Torus given Volume of Torus Sector Solution

Follow our step by step solution on how to calculate Radius of Circular Section of Torus given Volume of Torus Sector?

FIRST Step Consider the formula

r Circular Section = \sqrt{\frac{V Sector}{2 \cdot (π^{2}) \cdot (r) \cdot (\frac{∠ Intersection}{2 \cdot π})}}

Next Step Substitute values of Variables

∴

r Circular Section = \sqrt{\frac{1050m³}{2 \cdot (π^{2}) \cdot (10m) \cdot (\frac{30°}{2 \cdot π})}}

Next Step Substitute values of Constants

∴

r Circular Section = \sqrt{\frac{1050m³}{2 \cdot ({3.1416}^{2}) \cdot (10m) \cdot (\frac{30°}{2 \cdot 3.1416})}}

Next Step Convert Units

∴

r Circular Section = \sqrt{\frac{1050m³}{2 \cdot ({3.1416}^{2}) \cdot (10m) \cdot (\frac{0.5236rad}{2 \cdot 3.1416})}}

Next Step Prepare to Evaluate

∴

r Circular Section = \sqrt{\frac{1050}{2 \cdot ({3.1416}^{2}) \cdot (10) \cdot (\frac{0.5236}{2 \cdot 3.1416})}}

Next Step Evaluate

∴

r Circular Section = 7.98951473461842m

LAST Step Rounding Answer

∴

r Circular Section = 7.9895m

Radius of Circular Section of Torus given Volume of Torus Sector Formula Elements

Variables

Constants

Functions

Radius of Circular Section of Torus

Radius of Circular Section of Torus is the line connecting the center of the circular cross section to any point on the circumference of the circular cross section of the Torus.

Symbol: r_{Circular Section}

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Circular Section of Torus

Volume of Torus Sector

Volume of Torus Sector is the amount of three dimensional space occupied by Torus Sector.

Symbol: V_Sector

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Torus Sector

Radius of Torus

Radius of Torus is the line connecting the center of the overall Torus to the center of a circular cross-section of the Torus.

Symbol: r

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Torus

Angle of Intersection of Torus Sector

Angle of Intersection of Torus Sector is the angle subtended by the planes in which each of the circular end faces of the Torus Sector is contained.

Symbol: ∠_Intersection

Measurement: AngleUnit: °

Note: Value should be between 0 to 360.

Formulas to find Angle of Intersection of Torus 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

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Radius of Circular Section of Torus

Go Radius of Circular Section of Torus given Lateral Surface Area of Torus Sector

r Circular Section = (\frac{LSA Sector}{4 \cdot (π^{2}) \cdot (r) \cdot (\frac{∠ Intersection}{2 \cdot π})})

Other formulas in Radius of Circular Section of Torus category

Go Lateral Surface Area of Torus Sector

LSA Sector = (4 \cdot (π^{2}) \cdot (r) \cdot (r Circular Section) \cdot (\frac{∠ Intersection}{2 \cdot π}))

Go Lateral Surface Area of Torus Sector given Volume

LSA Sector = 2 \cdot (\frac{V Sector}{r Circular Section})

Go Total Surface Area of Torus Sector

TSA Sector = (LSA Sector + (2 \cdot π \cdot ({r Circular Section}^{2})))

Go Total Surface Area of Torus Sector given Lateral Surface Area and Radius

TSA Sector = (LSA Sector + (2 \cdot π \cdot ({(\frac{LSA Sector}{4 \cdot (π^{2}) \cdot (r) \cdot (\frac{∠ Intersection}{2 \cdot π})})}^{2})))

How to Evaluate Radius of Circular Section of Torus given Volume of Torus Sector?

Radius of Circular Section of Torus given Volume of Torus Sector evaluator uses Radius of Circular Section of Torus = sqrt(Volume of Torus Sector/(2*(pi^2)*(Radius of Torus)*(Angle of Intersection of Torus Sector/(2*pi)))) to evaluate the Radius of Circular Section of Torus, Radius of Circular Section of Torus given Volume of Torus Sector formula is defined as the line connecting the center of the circular cross section to any point on circumference of the circular cross section of Torus, calculated using volume of Torus Sector. Radius of Circular Section of Torus is denoted by r_{Circular Section} symbol.

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

FAQs on Radius of Circular Section of Torus given Volume of Torus Sector

What is the formula to find Radius of Circular Section of Torus given Volume of Torus Sector?

The formula of Radius of Circular Section of Torus given Volume of Torus Sector is expressed as Radius of Circular Section of Torus = sqrt(Volume of Torus Sector/(2*(pi^2)*(Radius of Torus)*(Angle of Intersection of Torus Sector/(2*pi)))). Here is an example- 7.989515 = sqrt(1050/(2*(pi^2)*(10)*(0.5235987755982/(2*pi)))).

How to calculate Radius of Circular Section of Torus given Volume of Torus Sector?

With Volume of Torus Sector (V_Sector), Radius of Torus (r) & Angle of Intersection of Torus Sector (∠_Intersection) we can find Radius of Circular Section of Torus given Volume of Torus Sector using the formula - Radius of Circular Section of Torus = sqrt(Volume of Torus Sector/(2*(pi^2)*(Radius of Torus)*(Angle of Intersection of Torus Sector/(2*pi)))). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Radius of Circular Section of Torus?

Here are the different ways to Calculate Radius of Circular Section of Torus-

Radius of Circular Section of Torus=(Lateral Surface Area of Torus Sector/(4*(pi^2)*(Radius of Torus)*(Angle of Intersection of Torus Sector/(2*pi))))

Can the Radius of Circular Section of Torus given Volume of Torus Sector be negative?

No, the Radius of Circular Section of Torus given Volume of Torus Sector, measured in Length cannot be negative.

Which unit is used to measure Radius of Circular Section of Torus given Volume of Torus Sector?

Radius of Circular Section of Torus given Volume of Torus 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 Circular Section of Torus given Volume of Torus Sector can be measured.

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Radius of Circular Section of Torus given Volume of Torus Sector Formula

​GoRadius of Circular Section of Torus given Lateral Surface Area of Torus Sector Formula

Radius of Circular Section of Torus given Volume of Torus Sector Example

Radius of Circular Section of Torus given Volume of Torus Sector Solution

Radius of Circular Section of Torus given Volume of Torus Sector Formula Elements

Other Formulas to find Radius of Circular Section of Torus

Other formulas in Radius of Circular Section of Torus category

How to Evaluate Radius of Circular Section of Torus given Volume of Torus Sector?

FAQs on Radius of Circular Section of Torus given Volume of Torus Sector

Variable Name

GoRadius of Circular Section of Torus given Lateral Surface Area of Torus Sector Formula