Surface to Volume Ratio of Toroid Sector Calculator

✖Radius of Toroid is the line connecting the center of the overall Toroid to the center of a cross-section of the Toroid.ⓘ Radius of Toroid [r]			+10% -10%
✖Cross Sectional Perimeter of Toroid is the total length of the boundary of the cross-section of the Toroid.ⓘ Cross Sectional Perimeter of Toroid [P_{Cross Section}]			+10% -10%
✖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.ⓘ Angle of Intersection of Toroid Sector [∠_Intersection]			+10% -10%
✖Cross Sectional Area of Toroid is the amount of two-dimensional space occupied by the cross-section of the Toroid.ⓘ Cross Sectional Area of Toroid [A_{Cross Section}]			+10% -10%

✖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.ⓘ Surface to Volume Ratio of Toroid Sector [R_A/V(Sector)]

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Formula

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Surface to Volume Ratio of Toroid Sector

Formula

`"R"_{"A/V(Sector)"} = ((2*pi*"r"*"P"_{"Cross Section"}*("∠"_{"Intersection"}/(2*pi)))+(2*"A"_{"Cross Section"}))/(2*pi*"r"*"A"_{"Cross Section"}*("∠"_{"Intersection"}/(2*pi)))`

Example

`"0.663662m⁻¹"=((2*pi*"10m"*"30m"*("180°"/(2*pi)))+(2*"50m²"))/(2*pi*"10m"*"50m²"*("180°"/(2*pi)))`

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Surface to Volume Ratio of Toroid Sector Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
R_A/V(Sector) = ((2*pi*r*P_{Cross Section}*(∠_Intersection/(2*pi)))+(2*A_{Cross Section}))/(2*pi*r*A_{Cross Section}*(∠_Intersection/(2*pi)))
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Surface to Volume Ratio of Toroid Sector - (Measured in 1 per Meter) - 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.
Radius of Toroid - (Measured in Meter) - Radius of Toroid is the line connecting the center of the overall Toroid to the center of a cross-section of the Toroid.
Cross Sectional Perimeter of Toroid - (Measured in Meter) - Cross Sectional Perimeter of Toroid is the total length of the boundary of the cross-section of the Toroid.
Angle of Intersection of Toroid Sector - (Measured in Radian) - 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.
Cross Sectional Area of Toroid - (Measured in Square Meter) - Cross Sectional Area of Toroid is the amount of two-dimensional space occupied by the cross-section of the Toroid.

STEP 1: Convert Input(s) to Base Unit

Radius of Toroid: 10 Meter --> 10 Meter No Conversion Required
Cross Sectional Perimeter of Toroid: 30 Meter --> 30 Meter No Conversion Required
Angle of Intersection of Toroid Sector: 180 Degree --> 3.1415926535892 Radian (Check conversion here)
Cross Sectional Area of Toroid: 50 Square Meter --> 50 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_A/V(Sector) = ((2*pi*r*P_{Cross Section}*(∠_Intersection/(2*pi)))+(2*A_{Cross Section}))/(2*pi*r*A_{Cross Section}*(∠_Intersection/(2*pi))) --> ((2*pi*10*30*(3.1415926535892/(2*pi)))+(2*50))/(2*pi*10*50*(3.1415926535892/(2*pi)))

Evaluating ... ...

R_A/V(Sector) = 0.66366197723677

STEP 3: Convert Result to Output's Unit

0.66366197723677 1 per Meter --> No Conversion Required

FINAL ANSWER

0.66366197723677 ≈ 0.663662 1 per Meter <-- Surface to Volume Ratio of Toroid Sector

(Calculation completed in 00.004 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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St Joseph's College (SJC), Bengaluru

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< 3 Surface to Volume Ratio Calculators

Surface to Volume Ratio of Toroid Sector

Go 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)))

Surface to Volume Ratio of Toroid given Total Surface Area

Go Surface to Volume Ratio of Toroid = (Total Surface Area of Toroid/(2*pi*Radius of Toroid*Cross Sectional Area of Toroid))

Surface to Volume Ratio of Toroid

Go Surface to Volume Ratio of Toroid = (Cross Sectional Perimeter of Toroid/Cross Sectional Area of Toroid)

Surface to Volume Ratio of Toroid Sector Formula

What is Toroid Sector?

Toroid Sector is a piece cut straight out of a toroid. The size of the piece is determined by the angle of intersection originating at the center. An angle of 360° covers the whole toroid.

What is Toroid?

In geometry, a Toroid is a surface of revolution with a hole in the middle. The axis of revolution passes through the hole and so does not intersect the surface. For example, when a rectangle is rotated around an axis parallel to one of its edges, then a hollow rectangle-section ring is produced. If the revolved figure is a circle, then the object is called a torus.

How to Calculate Surface to Volume Ratio of Toroid Sector?

Surface to Volume Ratio of Toroid Sector calculator 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 calculate 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 calculate Surface to Volume Ratio of Toroid Sector using this online calculator? To use this online calculator 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. Here is how the Surface to Volume Ratio of Toroid Sector calculation can be explained with given input values -> 0.663662 = ((2*pi*10*30*(3.1415926535892/(2*pi)))+(2*50))/(2*pi*10*50*(3.1415926535892/(2*pi))).

FAQ

What is 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 and is represented as R_A/V(Sector) = ((2*pi*r*P_{Cross Section}*(∠_Intersection/(2*pi)))+(2*A_{Cross Section}))/(2*pi*r*A_{Cross Section}*(∠_Intersection/(2*pi))) or 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))). Radius of Toroid is the line connecting the center of the overall Toroid to the center of a cross-section of the Toroid, Cross Sectional Perimeter of Toroid is the total length of the boundary of the cross-section of the Toroid, 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 & Cross Sectional Area of Toroid is the amount of two-dimensional space occupied by the cross-section of the Toroid.

How to calculate 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 is calculated using 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 calculate Surface to Volume Ratio of Toroid Sector, you need 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}). With our tool, you need to enter the respective value for Radius of Toroid, Cross Sectional Perimeter of Toroid, Angle of Intersection of Toroid Sector & Cross Sectional Area of Toroid and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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