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

✖Lateral Surface Area of Torus Sector is the total quantity of two-dimensional plane enclosed on the lateral curved surface of the Torus Sector.ⓘ Lateral Surface Area of Torus Sector [LSA_Sector]			+10% -10%
✖Radius of Torus is the line connecting the center of the overall Torus to the center of a circular cross-section of the Torus.ⓘ Radius of Torus [r]			+10% -10%
✖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.ⓘ Angle of Intersection of Torus Sector [∠_Intersection]			+10% -10%

✖Total Surface Area of Torus Sector is the total quantity of two dimensional space enclosed on the entire surface of the Torus Sector.ⓘ Total Surface Area of Torus Sector given Lateral Surface Area and Radius [TSA_Sector]

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Formula

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

Formula

`"TSA"_{"Sector"} = ("LSA"_{"Sector"}+(2*pi*(("LSA"_{"Sector"}/(4*(pi^2)*("r")*("∠"_{"Intersection"}/(2*pi))))^2)))`

Example

`"652.4367m²"=("260m²"+(2*pi*(("260m²"/(4*(pi^2)*("10m")*("30°"/(2*pi))))^2)))`

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

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Torus Sector = (Lateral Surface Area of Torus Sector+(2*pi*((Lateral Surface Area of Torus Sector/(4*(pi^2)*(Radius of Torus)*(Angle of Intersection of Torus Sector/(2*pi))))^2)))
TSA_Sector = (LSA_Sector+(2*pi*((LSA_Sector/(4*(pi^2)*(r)*(∠_Intersection/(2*pi))))^2)))
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Total Surface Area of Torus Sector - (Measured in Square Meter) - Total Surface Area of Torus Sector is the total quantity of two dimensional space enclosed on the entire surface of the Torus Sector.
Lateral Surface Area of Torus Sector - (Measured in Square Meter) - Lateral Surface Area of Torus Sector is the total quantity of two-dimensional plane enclosed on the lateral curved surface of the Torus Sector.
Radius of Torus - (Measured in Meter) - Radius of Torus is the line connecting the center of the overall Torus to the center of a circular cross-section of the Torus.
Angle of Intersection of Torus Sector - (Measured in Radian) - 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.

STEP 1: Convert Input(s) to Base Unit

Lateral Surface Area of Torus Sector: 260 Square Meter --> 260 Square Meter No Conversion Required
Radius of Torus: 10 Meter --> 10 Meter No Conversion Required
Angle of Intersection of Torus Sector: 30 Degree --> 0.5235987755982 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA_Sector = (LSA_Sector+(2*pi*((LSA_Sector/(4*(pi^2)*(r)*(∠_Intersection/(2*pi))))^2))) --> (260+(2*pi*((260/(4*(pi^2)*(10)*(0.5235987755982/(2*pi))))^2)))

Evaluating ... ...

TSA_Sector = 652.43667098332

STEP 3: Convert Result to Output's Unit

652.43667098332 Square Meter --> No Conversion Required

FINAL ANSWER

652.43667098332 ≈ 652.4367 Square Meter <-- Total Surface Area of Torus Sector

(Calculation completed in 00.007 seconds)

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< 2 Total Surface Area of Torus Sector Calculators

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

Go Total Surface Area of Torus Sector = (Lateral Surface Area of Torus Sector+(2*pi*((Lateral Surface Area of Torus Sector/(4*(pi^2)*(Radius of Torus)*(Angle of Intersection of Torus Sector/(2*pi))))^2)))

Total Surface Area of Torus Sector

Go Total Surface Area of Torus Sector = (Lateral Surface Area of Torus Sector+(2*pi*(Radius of Circular Section of Torus^2)))

< 9 Torus Sector Calculators

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

Volume of Torus Sector given Lateral Surface Area and Total Surface Area

Go Volume of Torus Sector = (2*(pi^2)*(Radius of Torus)*((Total Surface Area of Torus Sector-Lateral Surface Area of Torus Sector)/(2*pi))*(Angle of Intersection of Torus Sector/(2*pi)))

Radius of Circular Section of Torus given Volume of Torus Sector

Go 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))))

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

Go 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))))

Lateral Surface Area of Torus Sector

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

Volume of Torus Sector

Go Volume of Torus Sector = (2*(pi^2)*(Radius of Torus)*(Radius of Circular Section of Torus^2)*(Angle of Intersection of Torus Sector/(2*pi)))

Total Surface Area of Torus Sector

Go Total Surface Area of Torus Sector = (Lateral Surface Area of Torus Sector+(2*pi*(Radius of Circular Section of Torus^2)))

Lateral Surface Area of Torus Sector given Volume

Go Lateral Surface Area of Torus Sector = 2*(Volume of Torus Sector/(Radius of Circular Section of Torus))

Volume of Torus Sector given Lateral Surface Area

Go Volume of Torus Sector = (Radius of Circular Section of Torus*Lateral Surface Area of Torus Sector)/2

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

What is Torus Sector?

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

What is Torus?

In geometry, a Torus is a surface of revolution generated by revolving a circle in three-dimensional space about an axis that is coplanar with the circle. If the axis of revolution does not touch the circle, the surface has a ring shape and is called a torus of revolution.

How to Calculate Total Surface Area of Torus Sector given Lateral Surface Area and Radius?

Total Surface Area of Torus Sector given Lateral Surface Area and Radius calculator uses Total Surface Area of Torus Sector = (Lateral Surface Area of Torus Sector+(2*pi*((Lateral Surface Area of Torus Sector/(4*(pi^2)*(Radius of Torus)*(Angle of Intersection of Torus Sector/(2*pi))))^2))) to calculate the Total Surface Area of Torus Sector, Total Surface Area of Torus Sector given Lateral Surface Area and Radius formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Torus Sector, calculated using lateral surface area and radius of Torus Sector. Total Surface Area of Torus Sector is denoted by TSA_Sector symbol.

How to calculate Total Surface Area of Torus Sector given Lateral Surface Area and Radius using this online calculator? To use this online calculator for Total Surface Area of Torus Sector given Lateral Surface Area and Radius, enter Lateral Surface Area of Torus Sector (LSA_Sector), Radius of Torus (r) & Angle of Intersection of Torus Sector (∠_Intersection) and hit the calculate button. Here is how the Total Surface Area of Torus Sector given Lateral Surface Area and Radius calculation can be explained with given input values -> 652.4367 = (260+(2*pi*((260/(4*(pi^2)*(10)*(0.5235987755982/(2*pi))))^2))).

FAQ

What is Total Surface Area of Torus Sector given Lateral Surface Area and Radius?

Total Surface Area of Torus Sector given Lateral Surface Area and Radius formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Torus Sector, calculated using lateral surface area and radius of Torus Sector and is represented as TSA_Sector = (LSA_Sector+(2*pi*((LSA_Sector/(4*(pi^2)*(r)*(∠_Intersection/(2*pi))))^2))) or Total Surface Area of Torus Sector = (Lateral Surface Area of Torus Sector+(2*pi*((Lateral Surface Area of Torus Sector/(4*(pi^2)*(Radius of Torus)*(Angle of Intersection of Torus Sector/(2*pi))))^2))). Lateral Surface Area of Torus Sector is the total quantity of two-dimensional plane enclosed on the lateral curved surface of the Torus Sector, Radius of Torus is the line connecting the center of the overall Torus to the center of a circular cross-section of the Torus & 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.

How to calculate Total Surface Area of Torus Sector given Lateral Surface Area and Radius?

Total Surface Area of Torus Sector given Lateral Surface Area and Radius formula is defined as the total quantity of two dimensional space enclosed on the entire surface of the Torus Sector, calculated using lateral surface area and radius of Torus Sector is calculated using Total Surface Area of Torus Sector = (Lateral Surface Area of Torus Sector+(2*pi*((Lateral Surface Area of Torus Sector/(4*(pi^2)*(Radius of Torus)*(Angle of Intersection of Torus Sector/(2*pi))))^2))). To calculate Total Surface Area of Torus Sector given Lateral Surface Area and Radius, you need Lateral Surface Area of Torus Sector (LSA_Sector), Radius of Torus (r) & Angle of Intersection of Torus Sector (∠_Intersection). With our tool, you need to enter the respective value for Lateral Surface Area of Torus Sector, Radius of Torus & Angle of Intersection of Torus 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 Total Surface Area of Torus Sector?

In this formula, Total Surface Area of Torus Sector uses Lateral Surface Area of Torus Sector, Radius of Torus & Angle of Intersection of Torus Sector. We can use 2 other way(s) to calculate the same, which is/are as follows -

Total Surface Area of Torus Sector = (Lateral Surface Area of Torus Sector+(2*pi*(Radius of Circular Section of Torus^2)))
Total Surface Area of Torus Sector = (Lateral Surface Area of Torus Sector+(2*pi*(Radius of Circular Section of Torus^2)))

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