Radius of Circular Section of Torus given Volume of Torus Sector Calculator

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

✖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 given Volume of Torus Sector [r_{Circular Section}]

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Radius of Circular Section of Torus given Volume of Torus Sector Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

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.
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.
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

Volume of Torus Sector: 1050 Cubic Meter --> 1050 Cubic 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

r_{Circular Section} = sqrt(V_Sector/(2*(pi^2)*(r)*(∠_Intersection/(2*pi)))) --> sqrt(1050/(2*(pi^2)*(10)*(0.5235987755982/(2*pi))))

Evaluating ... ...

r_{Circular Section} = 7.98951473461842

STEP 3: Convert Result to Output's Unit

7.98951473461842 Meter --> No Conversion Required

FINAL ANSWER

7.98951473461842 ≈ 7.989515 Meter <-- Radius of Circular Section of Torus

(Calculation completed in 00.007 seconds)

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Walchand College of Engineering (WCE), Sangli

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< Radius of Circular Section of Torus Calculators

Radius of Circular Section of Torus given Volume of Torus Sector

LaTeX 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

LaTeX 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))))

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

LaTeX Go Radius of Circular Section of Torus = sqrt((Total Surface Area of Torus Sector-Lateral Surface Area of Torus Sector)/(2*pi))

< 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))

Radius of Circular Section of Torus given 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 Radius of Circular Section of Torus given Volume of Torus Sector?

Radius of Circular Section of Torus given Volume of Torus Sector calculator uses 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)))) to calculate the Radius of Circular Section of Torus, Radius of Circular Section of Torus given Volume of Torus Sector formula is defined as the line connecting the center of the circular cross section to any point on circumference of the circular cross section of Torus, calculated using volume of Torus Sector. Radius of Circular Section of Torus is denoted by r_{Circular Section} symbol.

How to calculate Radius of Circular Section of Torus given Volume of Torus Sector using this online calculator? To use this online calculator for Radius of Circular Section of Torus given Volume of Torus Sector, enter Volume of Torus Sector (V_Sector), Radius of Torus (r) & Angle of Intersection of Torus Sector (∠_Intersection) and hit the calculate button. Here is how the Radius of Circular Section of Torus given Volume of Torus Sector calculation can be explained with given input values -> 7.989515 = sqrt(1050/(2*(pi^2)*(10)*(0.5235987755982/(2*pi)))).

FAQ

What is Radius of Circular Section of Torus given Volume of Torus Sector?

Radius of Circular Section of Torus given Volume of Torus Sector formula is defined as the line connecting the center of the circular cross section to any point on circumference of the circular cross section of Torus, calculated using volume of Torus Sector and is represented as r_{Circular Section} = sqrt(V_Sector/(2*(pi^2)*(r)*(∠_Intersection/(2*pi)))) or 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)))). Volume of Torus Sector is the amount of three dimensional space occupied by 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 Radius of Circular Section of Torus given Volume of Torus Sector?

Radius of Circular Section of Torus given Volume of Torus Sector formula is defined as the line connecting the center of the circular cross section to any point on circumference of the circular cross section of Torus, calculated using volume of Torus Sector is calculated using 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)))). To calculate Radius of Circular Section of Torus given Volume of Torus Sector, you need Volume of Torus Sector (V_Sector), Radius of Torus (r) & Angle of Intersection of Torus Sector (∠_Intersection). With our tool, you need to enter the respective value for Volume 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 Radius of Circular Section of Torus?

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

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))))
Radius of Circular Section of Torus = sqrt((Total Surface Area of Torus Sector-Lateral Surface Area of Torus Sector)/(2*pi))
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))))

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