Surface to Volume Ratio of Cut Cylindrical Shell Calculator

✖Outer Radius of Cut Cylindrical Shell is the distance between center and any point on the circumference of the bottom circular face in the outer cut cylinder of the Cut Cylindrical Shell.ⓘ Outer Radius of Cut Cylindrical Shell [r_Outer]			+10% -10%
✖Short Outer Height of Cut Cylindrical Shell is the shortest vertical distance from the bottom circular face to the top elliptical face of the outer cut cylinder of the Cut Cylindrical Shell.ⓘ Short Outer Height of Cut Cylindrical Shell [h_{Short Outer}]			+10% -10%
✖Long Outer Height of Cut Cylindrical Shell is the longest vertical distance from the bottom circular face to the top elliptical face of the outer cut cylinder of the Cut Cylindrical Shell.ⓘ Long Outer Height of Cut Cylindrical Shell [h_{Long Outer}]			+10% -10%
✖Inner Radius of Cut Cylindrical Shell is the distance between center and any point on the circumference of the bottom circular face in the inner cut cylinder of the Cut Cylindrical Shell.ⓘ Inner Radius of Cut Cylindrical Shell [r_Inner]			+10% -10%
✖Short Inner Height of Cut Cylindrical Shell is the shortest vertical distance from the bottom circular face to the top elliptical face of the inner cut cylinder of the Cut Cylindrical Shell.ⓘ Short Inner Height of Cut Cylindrical Shell [h_{Short Inner}]			+10% -10%
✖Long Inner Height of Cut Cylindrical Shell is the longest vertical distance from the bottom circular face to the top elliptical face of the inner cut cylinder of the Cut Cylindrical Shell.ⓘ Long Inner Height of Cut Cylindrical Shell [h_{Long Inner}]			+10% -10%

✖Surface to Volume Ratio of Cut Cylindrical Shell is the numerical ratio of the total surface area of a Cut Cylindrical Shell to the volume of the Cut Cylindrical Shell.ⓘ Surface to Volume Ratio of Cut Cylindrical Shell [R_A/V]

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Surface to Volume Ratio of Cut Cylindrical Shell

Formula

`"R"_{"A/V"} = ((pi*(("r"_{"Outer"}*("h"_{"Short Outer"}+"h"_{"Long Outer"}))+("r"_{"Inner"}*("h"_{"Short Inner"}+"h"_{"Long Inner"}))))+(pi*("r"_{"Outer"}^2-"r"_{"Inner"}^2+("r"_{"Outer"}*sqrt("r"_{"Outer"}^2+(("h"_{"Long Outer"}-"h"_{"Short Outer"})/2)^2))-("r"_{"Inner"}*sqrt("r"_{"Inner"}^2+(("h"_{"Long Inner"}-"h"_{"Short Inner"})/2)^2)))))/(pi/2*(("r"_{"Outer"}^2*("h"_{"Short Outer"}+"h"_{"Long Outer"}))-("r"_{"Inner"}^2*("h"_{"Short Inner"}+"h"_{"Long Inner"}))))`

Example

`"0.612145m⁻¹"=((pi*(("12m"*("16m"+"20m"))+("8m"*("17m"+"19m"))))+(pi*(("12m")^2-("8m")^2+("12m"*sqrt(("12m")^2+(("20m"-"16m")/2)^2))-("8m"*sqrt(("8m")^2+(("19m"-"17m")/2)^2)))))/(pi/2*((("12m")^2*("16m"+"20m"))-(("8m")^2*("17m"+"19m"))))`

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Surface to Volume Ratio of Cut Cylindrical Shell Solution

STEP 0: Pre-Calculation Summary

Formula Used

Surface to Volume Ratio of Cut Cylindrical Shell = ((pi*((Outer Radius of Cut Cylindrical Shell*(Short Outer Height of Cut Cylindrical Shell+Long Outer Height of Cut Cylindrical Shell))+(Inner Radius of Cut Cylindrical Shell*(Short Inner Height of Cut Cylindrical Shell+Long Inner Height of Cut Cylindrical Shell))))+(pi*(Outer Radius of Cut Cylindrical Shell^2-Inner Radius of Cut Cylindrical Shell^2+(Outer Radius of Cut Cylindrical Shell*sqrt(Outer Radius of Cut Cylindrical Shell^2+((Long Outer Height of Cut Cylindrical Shell-Short Outer Height of Cut Cylindrical Shell)/2)^2))-(Inner Radius of Cut Cylindrical Shell*sqrt(Inner Radius of Cut Cylindrical Shell^2+((Long Inner Height of Cut Cylindrical Shell-Short Inner Height of Cut Cylindrical Shell)/2)^2)))))/(pi/2*((Outer Radius of Cut Cylindrical Shell^2*(Short Outer Height of Cut Cylindrical Shell+Long Outer Height of Cut Cylindrical Shell))-(Inner Radius of Cut Cylindrical Shell^2*(Short Inner Height of Cut Cylindrical Shell+Long Inner Height of Cut Cylindrical Shell))))
R_A/V = ((pi*((r_Outer*(h_{Short Outer}+h_{Long Outer}))+(r_Inner*(h_{Short Inner}+h_{Long Inner}))))+(pi*(r_Outer^2-r_Inner^2+(r_Outer*sqrt(r_Outer^2+((h_{Long Outer}-h_{Short Outer})/2)^2))-(r_Inner*sqrt(r_Inner^2+((h_{Long Inner}-h_{Short Inner})/2)^2)))))/(pi/2*((r_Outer^2*(h_{Short Outer}+h_{Long Outer}))-(r_Inner^2*(h_{Short Inner}+h_{Long Inner}))))
This formula uses 1 Constants, 1 Functions, 7 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

Surface to Volume Ratio of Cut Cylindrical Shell - (Measured in 1 per Meter) - Surface to Volume Ratio of Cut Cylindrical Shell is the numerical ratio of the total surface area of a Cut Cylindrical Shell to the volume of the Cut Cylindrical Shell.
Outer Radius of Cut Cylindrical Shell - (Measured in Meter) - Outer Radius of Cut Cylindrical Shell is the distance between center and any point on the circumference of the bottom circular face in the outer cut cylinder of the Cut Cylindrical Shell.
Short Outer Height of Cut Cylindrical Shell - (Measured in Meter) - Short Outer Height of Cut Cylindrical Shell is the shortest vertical distance from the bottom circular face to the top elliptical face of the outer cut cylinder of the Cut Cylindrical Shell.
Long Outer Height of Cut Cylindrical Shell - (Measured in Meter) - Long Outer Height of Cut Cylindrical Shell is the longest vertical distance from the bottom circular face to the top elliptical face of the outer cut cylinder of the Cut Cylindrical Shell.
Inner Radius of Cut Cylindrical Shell - (Measured in Meter) - Inner Radius of Cut Cylindrical Shell is the distance between center and any point on the circumference of the bottom circular face in the inner cut cylinder of the Cut Cylindrical Shell.
Short Inner Height of Cut Cylindrical Shell - (Measured in Meter) - Short Inner Height of Cut Cylindrical Shell is the shortest vertical distance from the bottom circular face to the top elliptical face of the inner cut cylinder of the Cut Cylindrical Shell.
Long Inner Height of Cut Cylindrical Shell - (Measured in Meter) - Long Inner Height of Cut Cylindrical Shell is the longest vertical distance from the bottom circular face to the top elliptical face of the inner cut cylinder of the Cut Cylindrical Shell.

STEP 1: Convert Input(s) to Base Unit

Outer Radius of Cut Cylindrical Shell: 12 Meter --> 12 Meter No Conversion Required
Short Outer Height of Cut Cylindrical Shell: 16 Meter --> 16 Meter No Conversion Required
Long Outer Height of Cut Cylindrical Shell: 20 Meter --> 20 Meter No Conversion Required
Inner Radius of Cut Cylindrical Shell: 8 Meter --> 8 Meter No Conversion Required
Short Inner Height of Cut Cylindrical Shell: 17 Meter --> 17 Meter No Conversion Required
Long Inner Height of Cut Cylindrical Shell: 19 Meter --> 19 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_A/V = ((pi*((r_Outer*(h_{Short Outer}+h_{Long Outer}))+(r_Inner*(h_{Short Inner}+h_{Long Inner}))))+(pi*(r_Outer^2-r_Inner^2+(r_Outer*sqrt(r_Outer^2+((h_{Long Outer}-h_{Short Outer})/2)^2))-(r_Inner*sqrt(r_Inner^2+((h_{Long Inner}-h_{Short Inner})/2)^2)))))/(pi/2*((r_Outer^2*(h_{Short Outer}+h_{Long Outer}))-(r_Inner^2*(h_{Short Inner}+h_{Long Inner})))) --> ((pi*((12*(16+20))+(8*(17+19))))+(pi*(12^2-8^2+(12*sqrt(12^2+((20-16)/2)^2))-(8*sqrt(8^2+((19-17)/2)^2)))))/(pi/2*((12^2*(16+20))-(8^2*(17+19))))

Evaluating ... ...

R_A/V = 0.612144610236645

STEP 3: Convert Result to Output's Unit

0.612144610236645 1 per Meter --> No Conversion Required

FINAL ANSWER

0.612144610236645 ≈ 0.612145 1 per Meter <-- Surface to Volume Ratio of Cut Cylindrical Shell

(Calculation completed in 00.020 seconds)

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< 1 Surface to Volume Ratio of Cut Cylindrical Shell Calculators

Surface to Volume Ratio of Cut Cylindrical Shell

Go Surface to Volume Ratio of Cut Cylindrical Shell = ((pi*((Outer Radius of Cut Cylindrical Shell*(Short Outer Height of Cut Cylindrical Shell+Long Outer Height of Cut Cylindrical Shell))+(Inner Radius of Cut Cylindrical Shell*(Short Inner Height of Cut Cylindrical Shell+Long Inner Height of Cut Cylindrical Shell))))+(pi*(Outer Radius of Cut Cylindrical Shell^2-Inner Radius of Cut Cylindrical Shell^2+(Outer Radius of Cut Cylindrical Shell*sqrt(Outer Radius of Cut Cylindrical Shell^2+((Long Outer Height of Cut Cylindrical Shell-Short Outer Height of Cut Cylindrical Shell)/2)^2))-(Inner Radius of Cut Cylindrical Shell*sqrt(Inner Radius of Cut Cylindrical Shell^2+((Long Inner Height of Cut Cylindrical Shell-Short Inner Height of Cut Cylindrical Shell)/2)^2)))))/(pi/2*((Outer Radius of Cut Cylindrical Shell^2*(Short Outer Height of Cut Cylindrical Shell+Long Outer Height of Cut Cylindrical Shell))-(Inner Radius of Cut Cylindrical Shell^2*(Short Inner Height of Cut Cylindrical Shell+Long Inner Height of Cut Cylindrical Shell))))

Surface to Volume Ratio of Cut Cylindrical Shell Formula

What is Cut Cylindrical Shell?

When a cylindrical shell is cut by a plane, across its lateral surface the resulting shape is called a Cut Cylindrical Shell. And if the cutting plane is parallel to the annular faces of the cylindrical shell then the resulting shapes are again cylindrical shells of smaller height. In general a Cut Cylindrical Shell has an annular face, two curved lateral surfaces one inside and one outside and an elliptical ring face, where that elliptical ring is the intersection of the cylindrical shell and the cutting plane.

How to Calculate Surface to Volume Ratio of Cut Cylindrical Shell?

Surface to Volume Ratio of Cut Cylindrical Shell calculator uses Surface to Volume Ratio of Cut Cylindrical Shell = ((pi*((Outer Radius of Cut Cylindrical Shell*(Short Outer Height of Cut Cylindrical Shell+Long Outer Height of Cut Cylindrical Shell))+(Inner Radius of Cut Cylindrical Shell*(Short Inner Height of Cut Cylindrical Shell+Long Inner Height of Cut Cylindrical Shell))))+(pi*(Outer Radius of Cut Cylindrical Shell^2-Inner Radius of Cut Cylindrical Shell^2+(Outer Radius of Cut Cylindrical Shell*sqrt(Outer Radius of Cut Cylindrical Shell^2+((Long Outer Height of Cut Cylindrical Shell-Short Outer Height of Cut Cylindrical Shell)/2)^2))-(Inner Radius of Cut Cylindrical Shell*sqrt(Inner Radius of Cut Cylindrical Shell^2+((Long Inner Height of Cut Cylindrical Shell-Short Inner Height of Cut Cylindrical Shell)/2)^2)))))/(pi/2*((Outer Radius of Cut Cylindrical Shell^2*(Short Outer Height of Cut Cylindrical Shell+Long Outer Height of Cut Cylindrical Shell))-(Inner Radius of Cut Cylindrical Shell^2*(Short Inner Height of Cut Cylindrical Shell+Long Inner Height of Cut Cylindrical Shell)))) to calculate the Surface to Volume Ratio of Cut Cylindrical Shell, Surface to Volume Ratio of Cut Cylindrical Shell formula is defined as the numerical ratio of the total surface area of a Cut Cylindrical Shell to the volume of the Cut Cylindrical Shell. Surface to Volume Ratio of Cut Cylindrical Shell is denoted by R_A/V symbol.

How to calculate Surface to Volume Ratio of Cut Cylindrical Shell using this online calculator? To use this online calculator for Surface to Volume Ratio of Cut Cylindrical Shell, enter Outer Radius of Cut Cylindrical Shell (r_Outer), Short Outer Height of Cut Cylindrical Shell (h_{Short Outer}), Long Outer Height of Cut Cylindrical Shell (h_{Long Outer}), Inner Radius of Cut Cylindrical Shell (r_Inner), Short Inner Height of Cut Cylindrical Shell (h_{Short Inner}) & Long Inner Height of Cut Cylindrical Shell (h_{Long Inner}) and hit the calculate button. Here is how the Surface to Volume Ratio of Cut Cylindrical Shell calculation can be explained with given input values -> 0.612145 = ((pi*((12*(16+20))+(8*(17+19))))+(pi*(12^2-8^2+(12*sqrt(12^2+((20-16)/2)^2))-(8*sqrt(8^2+((19-17)/2)^2)))))/(pi/2*((12^2*(16+20))-(8^2*(17+19)))).

FAQ

What is Surface to Volume Ratio of Cut Cylindrical Shell?

Surface to Volume Ratio of Cut Cylindrical Shell formula is defined as the numerical ratio of the total surface area of a Cut Cylindrical Shell to the volume of the Cut Cylindrical Shell and is represented as R_A/V = ((pi*((r_Outer*(h_{Short Outer}+h_{Long Outer}))+(r_Inner*(h_{Short Inner}+h_{Long Inner}))))+(pi*(r_Outer^2-r_Inner^2+(r_Outer*sqrt(r_Outer^2+((h_{Long Outer}-h_{Short Outer})/2)^2))-(r_Inner*sqrt(r_Inner^2+((h_{Long Inner}-h_{Short Inner})/2)^2)))))/(pi/2*((r_Outer^2*(h_{Short Outer}+h_{Long Outer}))-(r_Inner^2*(h_{Short Inner}+h_{Long Inner})))) or Surface to Volume Ratio of Cut Cylindrical Shell = ((pi*((Outer Radius of Cut Cylindrical Shell*(Short Outer Height of Cut Cylindrical Shell+Long Outer Height of Cut Cylindrical Shell))+(Inner Radius of Cut Cylindrical Shell*(Short Inner Height of Cut Cylindrical Shell+Long Inner Height of Cut Cylindrical Shell))))+(pi*(Outer Radius of Cut Cylindrical Shell^2-Inner Radius of Cut Cylindrical Shell^2+(Outer Radius of Cut Cylindrical Shell*sqrt(Outer Radius of Cut Cylindrical Shell^2+((Long Outer Height of Cut Cylindrical Shell-Short Outer Height of Cut Cylindrical Shell)/2)^2))-(Inner Radius of Cut Cylindrical Shell*sqrt(Inner Radius of Cut Cylindrical Shell^2+((Long Inner Height of Cut Cylindrical Shell-Short Inner Height of Cut Cylindrical Shell)/2)^2)))))/(pi/2*((Outer Radius of Cut Cylindrical Shell^2*(Short Outer Height of Cut Cylindrical Shell+Long Outer Height of Cut Cylindrical Shell))-(Inner Radius of Cut Cylindrical Shell^2*(Short Inner Height of Cut Cylindrical Shell+Long Inner Height of Cut Cylindrical Shell)))). Outer Radius of Cut Cylindrical Shell is the distance between center and any point on the circumference of the bottom circular face in the outer cut cylinder of the Cut Cylindrical Shell, Short Outer Height of Cut Cylindrical Shell is the shortest vertical distance from the bottom circular face to the top elliptical face of the outer cut cylinder of the Cut Cylindrical Shell, Long Outer Height of Cut Cylindrical Shell is the longest vertical distance from the bottom circular face to the top elliptical face of the outer cut cylinder of the Cut Cylindrical Shell, Inner Radius of Cut Cylindrical Shell is the distance between center and any point on the circumference of the bottom circular face in the inner cut cylinder of the Cut Cylindrical Shell, Short Inner Height of Cut Cylindrical Shell is the shortest vertical distance from the bottom circular face to the top elliptical face of the inner cut cylinder of the Cut Cylindrical Shell & Long Inner Height of Cut Cylindrical Shell is the longest vertical distance from the bottom circular face to the top elliptical face of the inner cut cylinder of the Cut Cylindrical Shell.

How to calculate Surface to Volume Ratio of Cut Cylindrical Shell?

Surface to Volume Ratio of Cut Cylindrical Shell formula is defined as the numerical ratio of the total surface area of a Cut Cylindrical Shell to the volume of the Cut Cylindrical Shell is calculated using Surface to Volume Ratio of Cut Cylindrical Shell = ((pi*((Outer Radius of Cut Cylindrical Shell*(Short Outer Height of Cut Cylindrical Shell+Long Outer Height of Cut Cylindrical Shell))+(Inner Radius of Cut Cylindrical Shell*(Short Inner Height of Cut Cylindrical Shell+Long Inner Height of Cut Cylindrical Shell))))+(pi*(Outer Radius of Cut Cylindrical Shell^2-Inner Radius of Cut Cylindrical Shell^2+(Outer Radius of Cut Cylindrical Shell*sqrt(Outer Radius of Cut Cylindrical Shell^2+((Long Outer Height of Cut Cylindrical Shell-Short Outer Height of Cut Cylindrical Shell)/2)^2))-(Inner Radius of Cut Cylindrical Shell*sqrt(Inner Radius of Cut Cylindrical Shell^2+((Long Inner Height of Cut Cylindrical Shell-Short Inner Height of Cut Cylindrical Shell)/2)^2)))))/(pi/2*((Outer Radius of Cut Cylindrical Shell^2*(Short Outer Height of Cut Cylindrical Shell+Long Outer Height of Cut Cylindrical Shell))-(Inner Radius of Cut Cylindrical Shell^2*(Short Inner Height of Cut Cylindrical Shell+Long Inner Height of Cut Cylindrical Shell)))). To calculate Surface to Volume Ratio of Cut Cylindrical Shell, you need Outer Radius of Cut Cylindrical Shell (r_Outer), Short Outer Height of Cut Cylindrical Shell (h_{Short Outer}), Long Outer Height of Cut Cylindrical Shell (h_{Long Outer}), Inner Radius of Cut Cylindrical Shell (r_Inner), Short Inner Height of Cut Cylindrical Shell (h_{Short Inner}) & Long Inner Height of Cut Cylindrical Shell (h_{Long Inner}). With our tool, you need to enter the respective value for Outer Radius of Cut Cylindrical Shell, Short Outer Height of Cut Cylindrical Shell, Long Outer Height of Cut Cylindrical Shell, Inner Radius of Cut Cylindrical Shell, Short Inner Height of Cut Cylindrical Shell & Long Inner Height of Cut Cylindrical Shell 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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