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)))
VSector = (2*(pi^2)*(r)*(rCircular 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
VSector = (2*(pi^2)*(r)*(rCircular Section^2)*(∠Intersection/(2*pi))) --> (2*(pi^2)*(10)*(8^2)*(0.5235987755982/(2*pi)))
Evaluating ... ...
VSector = 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 00.004 seconds)

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5 Volume of Torus Sector Calculators

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

9 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)))
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

Volume of Torus Sector Formula

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)))
VSector = (2*(pi^2)*(r)*(rCircular Section^2)*(Intersection/(2*pi)))

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 VSector 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 (rCircular 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 VSector = (2*(pi^2)*(r)*(rCircular 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 (rCircular 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 6 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)))
  • Volume of Torus Sector = (2*(pi^2)*(Lateral Surface Area of Torus Sector/(4*(pi^2)*(Radius of Circular Section of Torus)*(Angle of Intersection of Torus Sector/(2*pi))))*(Radius of Circular Section of Torus^2)*(Angle of Intersection of Torus Sector/(2*pi)))
  • 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)*((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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