Radius 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 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%

✖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 given Volume of Torus Sector [r]

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Radius of Torus given Volume of Torus Sector Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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 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

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

r = (V_Sector/(2*(pi^2)*(r_{Circular Section}^2)*(∠_Intersection/(2*pi)))) --> (1050/(2*(pi^2)*(8^2)*(0.5235987755982/(2*pi))))

Evaluating ... ...

r = 9.97380401479451

STEP 3: Convert Result to Output's Unit

9.97380401479451 Meter --> No Conversion Required

FINAL ANSWER

9.97380401479451 ≈ 9.973804 Meter <-- Radius of Torus

(Calculation completed in 00.004 seconds)

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< Radius of Torus Calculators

Radius of Torus given Lateral Surface Area of Torus Sector

LaTeX Go Radius of Torus = (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 Torus given Volume of Torus Sector

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

Radius of Torus given Volume of Torus Sector Formula

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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 Torus given Volume of Torus Sector?

Radius of Torus given Volume of Torus Sector calculator uses Radius of Torus = (Volume of Torus Sector/(2*(pi^2)*(Radius of Circular Section of Torus^2)*(Angle of Intersection of Torus Sector/(2*pi)))) to calculate the Radius of Torus, Radius of Torus given Volume of Torus Sector formula is defined as the line connecting the center of overall Torus to the center of circular cross section of Torus, calculated using volume of Torus Sector. Radius of Torus is denoted by r symbol.

How to calculate Radius of Torus given Volume of Torus Sector using this online calculator? To use this online calculator for Radius of Torus given Volume of Torus Sector, enter Volume of Torus Sector (V_Sector), 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 Radius of Torus given Volume of Torus Sector calculation can be explained with given input values -> 9.973804 = (1050/(2*(pi^2)*(8^2)*(0.5235987755982/(2*pi)))).

FAQ

What is Radius of Torus given Volume of Torus Sector?

Radius of Torus given Volume of Torus Sector formula is defined as the line connecting the center of overall Torus to the center of circular cross section of Torus, calculated using volume of Torus Sector and is represented as r = (V_Sector/(2*(pi^2)*(r_{Circular Section}^2)*(∠_Intersection/(2*pi)))) or Radius of Torus = (Volume of Torus Sector/(2*(pi^2)*(Radius of Circular Section of Torus^2)*(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 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 Radius of Torus given Volume of Torus Sector?

Radius of Torus given Volume of Torus Sector formula is defined as the line connecting the center of overall Torus to the center of circular cross section of Torus, calculated using volume of Torus Sector is calculated using Radius of Torus = (Volume of Torus Sector/(2*(pi^2)*(Radius of Circular Section of Torus^2)*(Angle of Intersection of Torus Sector/(2*pi)))). To calculate Radius of Torus given Volume of Torus Sector, you need Volume of Torus Sector (V_Sector), 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 Volume of Torus Sector, 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 Radius of Torus?

In this formula, Radius of Torus uses Volume of Torus Sector, Radius of Circular Section of Torus & Angle of Intersection of Torus Sector. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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