Radius of Toroid given Total Surface Area of Toroid Sector Calculator

✖Total Surface Area of Toroid Sector is the total quantity of two-dimensional space enclosed on the entire surface of the Toroid Sector.ⓘ Total Surface Area of Toroid Sector [TSA_Sector]			+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%
✖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%

✖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 given Total Surface Area of Toroid Sector [r]

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Formula

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Radius of Toroid given Total Surface Area of Toroid Sector

Formula

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

Example

`"10.07981m"=("1050m²"-(2*"50m²"))/(2*pi*"30m"*("180°"/(2*pi)))`

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Radius of Toroid given Total Surface Area of Toroid Sector Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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.
Total Surface Area of Toroid Sector - (Measured in Square Meter) - Total Surface Area of Toroid Sector is the total quantity of two-dimensional space enclosed on the entire surface of the Toroid Sector.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Total Surface Area of Toroid Sector: 1050 Square Meter --> 1050 Square Meter No Conversion Required
Cross Sectional Area of Toroid: 50 Square Meter --> 50 Square 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)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r = (TSA_Sector-(2*A_{Cross Section}))/(2*pi*P_{Cross Section}*(∠_Intersection/(2*pi))) --> (1050-(2*50))/(2*pi*30*(3.1415926535892/(2*pi)))

Evaluating ... ...

r = 10.0798130624886

STEP 3: Convert Result to Output's Unit

10.0798130624886 Meter --> No Conversion Required

FINAL ANSWER

10.0798130624886 ≈ 10.07981 Meter <-- Radius of Toroid

(Calculation completed in 00.020 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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< 5 Toroid Sector Calculators

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

Go Cross Sectional Perimeter of Toroid = (Total Surface Area of Toroid Sector-(2*Cross Sectional Area of Toroid))/(2*pi*Radius of Toroid*(Angle of Intersection of Toroid Sector/(2*pi)))

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

Go Cross Sectional Area of Toroid = ((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)

Radius of Toroid given Total Surface Area of Toroid Sector

Go 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)))

Cross Sectional Area of Toroid given Volume of Toroid Sector

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

Radius of Toroid given Volume of Toroid Sector

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

Radius of Toroid given Total Surface Area 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 Radius of Toroid given Total Surface Area of Toroid Sector?

Radius of Toroid given Total Surface Area of Toroid Sector calculator 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 calculate 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 calculate Radius of Toroid given Total Surface Area of Toroid Sector using this online calculator? To use this online calculator 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. Here is how the Radius of Toroid given Total Surface Area of Toroid Sector calculation can be explained with given input values -> 10.07981 = (1050-(2*50))/(2*pi*30*(3.1415926535892/(2*pi))).

FAQ

What is Radius of Toroid given Total Surface Area of Toroid Sector?

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 and is represented as r = (TSA_Sector-(2*A_{Cross Section}))/(2*pi*P_{Cross Section}*(∠_Intersection/(2*pi))) or 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))). Total Surface Area of Toroid Sector is the total quantity of two-dimensional space enclosed on the entire surface of the Toroid Sector, Cross Sectional Area of Toroid is the amount of two-dimensional space occupied by the 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.

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

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

How many ways are there to calculate Radius of Toroid?

In this formula, Radius of Toroid uses Total Surface Area of Toroid Sector, Cross Sectional Area of Toroid, Cross Sectional Perimeter of Toroid & Angle of Intersection of Toroid Sector. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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