Surface to Volume Ratio of Toroid Sector Solution

STEP 0: Pre-Calculation Summary
Formula Used
Surface to Volume Ratio of Toroid Sector = ((2*pi*Radius of Toroid*Cross Sectional Perimeter of Toroid*(Angle of Intersection of Toroid Sector/(2*pi)))+(2*Cross Sectional Area of Toroid))/(2*pi*Radius of Toroid*Cross Sectional Area of Toroid*(Angle of Intersection of Toroid Sector/(2*pi)))
RA/V(Sector) = ((2*pi*r*PCross Section*(Intersection/(2*pi)))+(2*ACross Section))/(2*pi*r*ACross Section*(Intersection/(2*pi)))
This formula uses 1 Constants, 5 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Surface to Volume Ratio of Toroid Sector - (Measured in 1 per Meter) - Surface to Volume Ratio of Toroid Sector is the numerical ratio of the total surface area of the Toroid Sector to the volume of the Toroid Sector.
Radius of Toroid - (Measured in Meter) - Radius of Toroid is the line connecting the center of the overall Toroid to the center of a cross-section of the Toroid.
Cross Sectional Perimeter of Toroid - (Measured in Meter) - Cross Sectional Perimeter of Toroid is the total length of the boundary of the cross-section of the Toroid.
Angle of Intersection of Toroid Sector - (Measured in Radian) - Angle of Intersection of Toroid Sector is the angle subtended by the planes in which each of the circular end faces of the Toroid Sector is contained.
Cross Sectional Area of Toroid - (Measured in Square Meter) - Cross Sectional Area of Toroid is the amount of two-dimensional space occupied by the cross-section of the Toroid.
STEP 1: Convert Input(s) to Base Unit
Radius of Toroid: 10 Meter --> 10 Meter No Conversion Required
Cross Sectional Perimeter of Toroid: 30 Meter --> 30 Meter No Conversion Required
Angle of Intersection of Toroid Sector: 180 Degree --> 3.1415926535892 Radian (Check conversion ​here)
Cross Sectional Area of Toroid: 50 Square Meter --> 50 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
RA/V(Sector) = ((2*pi*r*PCross Section*(∠Intersection/(2*pi)))+(2*ACross Section))/(2*pi*r*ACross Section*(∠Intersection/(2*pi))) --> ((2*pi*10*30*(3.1415926535892/(2*pi)))+(2*50))/(2*pi*10*50*(3.1415926535892/(2*pi)))
Evaluating ... ...
RA/V(Sector) = 0.66366197723677
STEP 3: Convert Result to Output's Unit
0.66366197723677 1 per Meter --> No Conversion Required
FINAL ANSWER
0.66366197723677 0.663662 1 per Meter <-- Surface to Volume Ratio of Toroid Sector
(Calculation completed in 00.013 seconds)

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Created by Shweta Patil
Walchand College of Engineering (WCE), Sangli
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Surface to Volume Ratio Calculators

Surface to Volume Ratio of Toroid Sector
​ LaTeX ​ Go Surface to Volume Ratio of Toroid Sector = ((2*pi*Radius of Toroid*Cross Sectional Perimeter of Toroid*(Angle of Intersection of Toroid Sector/(2*pi)))+(2*Cross Sectional Area of Toroid))/(2*pi*Radius of Toroid*Cross Sectional Area of Toroid*(Angle of Intersection of Toroid Sector/(2*pi)))
Surface to Volume Ratio of Toroid given Total Surface Area
​ LaTeX ​ Go Surface to Volume Ratio of Toroid = (Total Surface Area of Toroid/(2*pi*Radius of Toroid*Cross Sectional Area of Toroid))
Surface to Volume Ratio of Toroid
​ LaTeX ​ Go Surface to Volume Ratio of Toroid = (Cross Sectional Perimeter of Toroid/Cross Sectional Area of Toroid)

Surface to Volume Ratio of Toroid Sector Formula

​LaTeX ​Go
Surface to Volume Ratio of Toroid Sector = ((2*pi*Radius of Toroid*Cross Sectional Perimeter of Toroid*(Angle of Intersection of Toroid Sector/(2*pi)))+(2*Cross Sectional Area of Toroid))/(2*pi*Radius of Toroid*Cross Sectional Area of Toroid*(Angle of Intersection of Toroid Sector/(2*pi)))
RA/V(Sector) = ((2*pi*r*PCross Section*(Intersection/(2*pi)))+(2*ACross Section))/(2*pi*r*ACross Section*(Intersection/(2*pi)))

What is Toroid Sector?

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

What is Toroid?

In geometry, a Toroid is a surface of revolution with a hole in the middle. The axis of revolution passes through the hole and so does not intersect the surface. For example, when a rectangle is rotated around an axis parallel to one of its edges, then a hollow rectangle-section ring is produced. If the revolved figure is a circle, then the object is called a torus.

How to Calculate Surface to Volume Ratio of Toroid Sector?

Surface to Volume Ratio of Toroid Sector calculator uses Surface to Volume Ratio of Toroid Sector = ((2*pi*Radius of Toroid*Cross Sectional Perimeter of Toroid*(Angle of Intersection of Toroid Sector/(2*pi)))+(2*Cross Sectional Area of Toroid))/(2*pi*Radius of Toroid*Cross Sectional Area of Toroid*(Angle of Intersection of Toroid Sector/(2*pi))) to calculate the Surface to Volume Ratio of Toroid Sector, Surface to Volume Ratio of Toroid Sector formula is defined as the numerical ratio of the total surface area of the Toroid Sector to the volume of the Toroid Sector. Surface to Volume Ratio of Toroid Sector is denoted by RA/V(Sector) symbol.

How to calculate Surface to Volume Ratio of Toroid Sector using this online calculator? To use this online calculator for Surface to Volume Ratio of Toroid Sector, enter Radius of Toroid (r), Cross Sectional Perimeter of Toroid (PCross Section), Angle of Intersection of Toroid Sector (∠Intersection) & Cross Sectional Area of Toroid (ACross Section) and hit the calculate button. Here is how the Surface to Volume Ratio of Toroid Sector calculation can be explained with given input values -> 0.663662 = ((2*pi*10*30*(3.1415926535892/(2*pi)))+(2*50))/(2*pi*10*50*(3.1415926535892/(2*pi))).

FAQ

What is Surface to Volume Ratio of Toroid Sector?
Surface to Volume Ratio of Toroid Sector formula is defined as the numerical ratio of the total surface area of the Toroid Sector to the volume of the Toroid Sector and is represented as RA/V(Sector) = ((2*pi*r*PCross Section*(∠Intersection/(2*pi)))+(2*ACross Section))/(2*pi*r*ACross Section*(∠Intersection/(2*pi))) or Surface to Volume Ratio of Toroid Sector = ((2*pi*Radius of Toroid*Cross Sectional Perimeter of Toroid*(Angle of Intersection of Toroid Sector/(2*pi)))+(2*Cross Sectional Area of Toroid))/(2*pi*Radius of Toroid*Cross Sectional Area of Toroid*(Angle of Intersection of Toroid Sector/(2*pi))). Radius of Toroid is the line connecting the center of the overall Toroid to the center of a cross-section of the Toroid, Cross Sectional Perimeter of Toroid is the total length of the boundary of the cross-section of the Toroid, Angle of Intersection of Toroid Sector is the angle subtended by the planes in which each of the circular end faces of the Toroid Sector is contained & Cross Sectional Area of Toroid is the amount of two-dimensional space occupied by the cross-section of the Toroid.
How to calculate Surface to Volume Ratio of Toroid Sector?
Surface to Volume Ratio of Toroid Sector formula is defined as the numerical ratio of the total surface area of the Toroid Sector to the volume of the Toroid Sector is calculated using Surface to Volume Ratio of Toroid Sector = ((2*pi*Radius of Toroid*Cross Sectional Perimeter of Toroid*(Angle of Intersection of Toroid Sector/(2*pi)))+(2*Cross Sectional Area of Toroid))/(2*pi*Radius of Toroid*Cross Sectional Area of Toroid*(Angle of Intersection of Toroid Sector/(2*pi))). To calculate Surface to Volume Ratio of Toroid Sector, you need Radius of Toroid (r), Cross Sectional Perimeter of Toroid (PCross Section), Angle of Intersection of Toroid Sector (∠Intersection) & Cross Sectional Area of Toroid (ACross Section). With our tool, you need to enter the respective value for Radius of Toroid, Cross Sectional Perimeter of Toroid, Angle of Intersection of Toroid Sector & Cross Sectional Area of Toroid and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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