Volume of Torus Sector Calculator

✖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%
✖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.ⓘ Radius of Circular Section of Torus [r_{Circular Section}]			+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%

✖Volume of Torus Sector is the amount of three dimensional space occupied by Torus Sector.ⓘ Volume of Torus Sector [V_Sector]

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Volume of Torus Sector Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
V_Sector = (2*(pi^2)*(r)*(r_{Circular Section}^2)*(∠_Intersection/(2*pi)))
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Volume of Torus Sector - (Measured in Cubic Meter) - Volume of Torus Sector is the amount of three dimensional space occupied by 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.
Radius of Circular Section of Torus - (Measured in Meter) - 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.
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

Radius of Torus: 10 Meter --> 10 Meter No Conversion Required
Radius of Circular Section of Torus: 8 Meter --> 8 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

V_Sector = (2*(pi^2)*(r)*(r_{Circular Section}^2)*(∠_Intersection/(2*pi))) --> (2*(pi^2)*(10)*(8^2)*(0.5235987755982/(2*pi)))

Evaluating ... ...

V_Sector = 1052.75780278267

STEP 3: Convert Result to Output's Unit

1052.75780278267 Cubic Meter --> No Conversion Required

FINAL ANSWER

1052.75780278267 ≈ 1052.758 Cubic Meter <-- Volume of Torus Sector

(Calculation completed in 00.020 seconds)

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< Volume of Torus Sector Calculators

Volume of Torus Sector given Lateral Surface Area and Radius

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

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

LaTeX 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)))

Volume of Torus Sector

LaTeX 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)))

Volume of Torus Sector given Lateral Surface Area

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

< Torus Sector Calculators

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

LaTeX 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)))

Lateral Surface Area of Torus Sector

LaTeX 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)))

Total Surface Area of Torus Sector

LaTeX 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

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

Volume of Torus Sector Formula

LaTeX Go

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 Volume of Torus Sector?

Volume of Torus Sector calculator uses 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))) to calculate the Volume of Torus Sector, Volume of Torus Sector formula is defined as amount of three dimensional space covered by Torus Sector. Volume of Torus Sector is denoted by V_Sector symbol.

How to calculate Volume of Torus Sector using this online calculator? To use this online calculator for Volume of Torus Sector, enter Radius of Torus (r), Radius of Circular Section of Torus (r_{Circular Section}) & Angle of Intersection of Torus Sector (∠_Intersection) and hit the calculate button. Here is how the Volume of Torus Sector calculation can be explained with given input values -> 1052.758 = (2*(pi^2)*(10)*(8^2)*(0.5235987755982/(2*pi))).

FAQ

What is Volume of Torus Sector?

Volume of Torus Sector formula is defined as amount of three dimensional space covered by Torus Sector and is represented as V_Sector = (2*(pi^2)*(r)*(r_{Circular Section}^2)*(∠_Intersection/(2*pi))) or 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))). 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 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 & 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 Volume of Torus Sector?

Volume of Torus Sector formula is defined as amount of three dimensional space covered by Torus Sector is calculated using 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))). To calculate Volume of Torus Sector, you need Radius of Torus (r), Radius of Circular Section of Torus (r_{Circular Section}) & Angle of Intersection of Torus Sector (∠_Intersection). With our tool, you need to enter the respective value for Radius of Torus, Radius of Circular Section 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 Volume of Torus Sector?

In this formula, Volume of Torus Sector uses Radius of Torus, Radius of Circular Section of Torus & Angle of Intersection of Torus Sector. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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