Total Surface Area of Toroid Sector Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
TSASector = ((2*pi*r*PCross Section)*(Intersection/(2*pi)))+(2*ACross Section)
This formula uses 1 Constants, 5 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
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.
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
TSASector = ((2*pi*r*PCross Section)*(∠Intersection/(2*pi)))+(2*ACross Section) --> ((2*pi*10*30)*(3.1415926535892/(2*pi)))+(2*50)
Evaluating ... ...
TSASector = 1042.47779607676
STEP 3: Convert Result to Output's Unit
1042.47779607676 Square Meter --> No Conversion Required
FINAL ANSWER
1042.47779607676 1042.478 Square Meter <-- Total Surface Area of Toroid Sector
(Calculation completed in 00.004 seconds)

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Walchand College of Engineering (WCE), Sangli
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4 Total Surface Area of Toroid Sector Calculators

Total Surface Area of Toroid Sector given Volume of Toroid Sector
Go 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 given Volume and Angle of Intersection
Go 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)))))
Total Surface Area of Toroid Sector given Volume
Go 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)
Total Surface Area of Toroid Sector
Go 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)

7 Toroid Sector Calculators

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

Total Surface Area of Toroid Sector 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*Cross Sectional Area of Toroid)
TSASector = ((2*pi*r*PCross Section)*(Intersection/(2*pi)))+(2*ACross Section)

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 Total Surface Area of Toroid Sector?

Total Surface Area of Toroid Sector calculator 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*Cross Sectional Area of Toroid) to calculate the Total Surface Area of Toroid Sector, The Total Surface Area of Toroid Sector formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Toroid Sector. Total Surface Area of Toroid Sector is denoted by TSASector symbol.

How to calculate Total Surface Area of Toroid Sector using this online calculator? To use this online calculator for Total Surface Area of Toroid Sector, enter Radius of Toroid (r), Cross Sectional Perimeter of Toroid (PCross Section), Angle of Intersection of Toroid Sector (∠Intersection) & Cross Sectional Area of Toroid (ACross Section) and hit the calculate button. Here is how the Total Surface Area of Toroid Sector calculation can be explained with given input values -> 1042.478 = ((2*pi*10*30)*(3.1415926535892/(2*pi)))+(2*50).

FAQ

What is Total Surface Area of Toroid Sector?
The Total Surface Area of Toroid Sector formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Toroid Sector and is represented as TSASector = ((2*pi*r*PCross Section)*(∠Intersection/(2*pi)))+(2*ACross Section) or 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). 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 Total Surface Area of Toroid Sector?
The Total Surface Area of Toroid Sector formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Toroid Sector is calculated using 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). To calculate Total Surface Area of Toroid Sector, you need Radius of Toroid (r), Cross Sectional Perimeter of Toroid (PCross Section), Angle of Intersection of Toroid Sector (∠Intersection) & Cross Sectional Area of Toroid (ACross 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.
How many ways are there to calculate Total Surface Area of Toroid Sector?
In this formula, Total Surface Area of Toroid Sector uses Radius of Toroid, Cross Sectional Perimeter of Toroid, Angle of Intersection of Toroid Sector & Cross Sectional Area of Toroid. We can use 4 other way(s) to calculate the same, which is/are as follows -
  • 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)
  • 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)))))
  • 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)
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