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Surface to volume ratio of Cut Cylindrical Shell Solution

STEP 0: Pre-Calculation Summary
Formula Used
surface_to_volume_ratio = (Lateral Surface Area Polyhedron+(pi*((Radius 1^2)-(Radius^2)+(Radius 1*(sqrt((Radius 1^2)+(((Long outer height-Short outer height)/2)^2))))- (Radius*(sqrt((Radius^2)+(((Long inner height-Short inner height)/2)^2)))))))/((pi/2)*(((Radius 1^2)*(Short outer height+Long outer height))-((Radius^2)*(Short inner height+Long inner height))))
RAV = (SALateral_Polyhedron+(pi*((r1^2)-(r^2)+(r1*(sqrt((r1^2)+(((hOuter_long-hOuter_short)/2)^2))))- (r*(sqrt((r^2)+(((hInner_long-hInner_short)/2)^2)))))))/((pi/2)*(((r1^2)*(hOuter_short+hOuter_long))-((r^2)*(hInner_short+hInner_long))))
This formula uses 1 Constants, 1 Functions, 7 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Lateral Surface Area Polyhedron - Lateral Surface Area Polyhedron is the area of the lateral surface of any polyhedron. (Measured in Square Meter)
Radius 1 - Radius 1 is a radial line from the focus to any point of a curve. (Measured in Meter)
Radius - Radius is a radial line from the focus to any point of a curve. (Measured in Meter)
Long outer height - Long outer height is the long height of outer body of a shape or figure. (Measured in Meter)
Short outer height - Short outer height is the short height of outer body of a shape or figure. (Measured in Meter)
Long inner height - Long inner height is the long height of outer body of a shape or figure. (Measured in Meter)
Short inner height - Short inner height is the short height of inner body of a shape or figure. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Lateral Surface Area Polyhedron: 2000 Square Meter --> 2000 Square Meter No Conversion Required
Radius 1: 11 Meter --> 11 Meter No Conversion Required
Radius: 10 Meter --> 10 Meter No Conversion Required
Long outer height: 16 Meter --> 16 Meter No Conversion Required
Short outer height: 12 Meter --> 12 Meter No Conversion Required
Long inner height: 15.9 Meter --> 15.9 Meter No Conversion Required
Short inner height: 12.1 Meter --> 12.1 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
RAV = (SALateral_Polyhedron+(pi*((r1^2)-(r^2)+(r1*(sqrt((r1^2)+(((hOuter_long-hOuter_short)/2)^2))))- (r*(sqrt((r^2)+(((hInner_long-hInner_short)/2)^2)))))))/((pi/2)*(((r1^2)*(hOuter_short+hOuter_long))-((r^2)*(hInner_short+hInner_long)))) --> (2000+(pi*((11^2)-(10^2)+(11*(sqrt((11^2)+(((16-12)/2)^2))))- (10*(sqrt((10^2)+(((15.9-12.1)/2)^2)))))))/((pi/2)*(((11^2)*(12+16))-((10^2)*(12.1+15.9))))
Evaluating ... ...
RAV = 2.30889290370505
STEP 3: Convert Result to Output's Unit
2.30889290370505 Hundred --> No Conversion Required
FINAL ANSWER
2.30889290370505 Hundred <-- Surface to Volume Ratio
(Calculation completed in 00.047 seconds)

4 Surface area, Volume and Surface to volume ratio of Cut Cylindrical Shell Calculators

Surface to volume ratio of Cut Cylindrical Shell
surface_to_volume_ratio = (Lateral Surface Area Polyhedron+(pi*((Radius 1^2)-(Radius^2)+(Radius 1*(sqrt((Radius 1^2)+(((Long outer height-Short outer height)/2)^2))))- (Radius*(sqrt((Radius^2)+(((Long inner height-Short inner height)/2)^2)))))))/((pi/2)*(((Radius 1^2)*(Short outer height+Long outer height))-((Radius^2)*(Short inner height+Long inner height)))) Go
Surface area of Cut Cylindrical Shell missing lateral surface area
surface_area_of_polyhedron = (pi*((Radius 1*(Short outer height+Long outer height))+(Radius*(Short inner height+Long inner height))))+(pi*((Radius 1^2)-(Radius^2)+(Radius 1*(sqrt((Radius 1^2)+(((Long outer height-Short outer height)/2)^2))))- (Radius*(sqrt((Radius^2)+(((Long inner height-Short inner height)/2)^2)))))) Go
Surface area of Cut Cylindrical Shell
surface_area_of_polyhedron = Lateral Surface Area Polyhedron+(pi*((Radius 1^2)-(Radius^2)+(Radius 1*(sqrt((Radius 1^2)+(((Long outer height-Short outer height)/2)^2))))- (Radius*(sqrt((Radius^2)+(((Long inner height-Short inner height)/2)^2)))))) Go
Volume of Cut Cylindrical Shell
volume_polyhedron = (pi/2)*(((Radius 1^2)*(Short outer height+Long outer height))-((Radius^2)*(Short inner height+Long inner height))) Go

Surface to volume ratio of Cut Cylindrical Shell Formula

surface_to_volume_ratio = (Lateral Surface Area Polyhedron+(pi*((Radius 1^2)-(Radius^2)+(Radius 1*(sqrt((Radius 1^2)+(((Long outer height-Short outer height)/2)^2))))- (Radius*(sqrt((Radius^2)+(((Long inner height-Short inner height)/2)^2)))))))/((pi/2)*(((Radius 1^2)*(Short outer height+Long outer height))-((Radius^2)*(Short inner height+Long inner height))))
RAV = (SALateral_Polyhedron+(pi*((r1^2)-(r^2)+(r1*(sqrt((r1^2)+(((hOuter_long-hOuter_short)/2)^2))))- (r*(sqrt((r^2)+(((hInner_long-hInner_short)/2)^2)))))))/((pi/2)*(((r1^2)*(hOuter_short+hOuter_long))-((r^2)*(hInner_short+hInner_long))))

What is Cut Cylindrical Shell?

A cut cylindrical shell is a cut cylinder, from which in its center a narrower cut cylinder of the same central height is removed. Its slice plane has annulus and elliptical ring.

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 = (Lateral Surface Area Polyhedron+(pi*((Radius 1^2)-(Radius^2)+(Radius 1*(sqrt((Radius 1^2)+(((Long outer height-Short outer height)/2)^2))))- (Radius*(sqrt((Radius^2)+(((Long inner height-Short inner height)/2)^2)))))))/((pi/2)*(((Radius 1^2)*(Short outer height+Long outer height))-((Radius^2)*(Short inner height+Long inner height)))) to calculate the Surface to Volume Ratio, The Surface to volume ratio of Cut Cylindrical Shell formula is defined as ratio of surface area to volume of cut cylindrical shell. Surface to Volume Ratio is denoted by RAV 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 Lateral Surface Area Polyhedron (SALateral_Polyhedron), Radius 1 (r1), Radius (r), Long outer height (hOuter_long), Short outer height (hOuter_short), Long inner height (hInner_long) & Short inner height (hInner_short) 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 -> 2.308893 = (2000+(pi*((11^2)-(10^2)+(11*(sqrt((11^2)+(((16-12)/2)^2))))- (10*(sqrt((10^2)+(((15.9-12.1)/2)^2)))))))/((pi/2)*(((11^2)*(12+16))-((10^2)*(12.1+15.9)))).

FAQ

What is Surface to volume ratio of Cut Cylindrical Shell?
The Surface to volume ratio of Cut Cylindrical Shell formula is defined as ratio of surface area to volume of cut cylindrical shell and is represented as RAV = (SALateral_Polyhedron+(pi*((r1^2)-(r^2)+(r1*(sqrt((r1^2)+(((hOuter_long-hOuter_short)/2)^2))))- (r*(sqrt((r^2)+(((hInner_long-hInner_short)/2)^2)))))))/((pi/2)*(((r1^2)*(hOuter_short+hOuter_long))-((r^2)*(hInner_short+hInner_long)))) or surface_to_volume_ratio = (Lateral Surface Area Polyhedron+(pi*((Radius 1^2)-(Radius^2)+(Radius 1*(sqrt((Radius 1^2)+(((Long outer height-Short outer height)/2)^2))))- (Radius*(sqrt((Radius^2)+(((Long inner height-Short inner height)/2)^2)))))))/((pi/2)*(((Radius 1^2)*(Short outer height+Long outer height))-((Radius^2)*(Short inner height+Long inner height)))). Lateral Surface Area Polyhedron is the area of the lateral surface of any polyhedron, Radius 1 is a radial line from the focus to any point of a curve, Radius is a radial line from the focus to any point of a curve, Long outer height is the long height of outer body of a shape or figure, Short outer height is the short height of outer body of a shape or figure, Long inner height is the long height of outer body of a shape or figure & Short inner height is the short height of inner body of a shape or figure.
How to calculate Surface to volume ratio of Cut Cylindrical Shell?
The Surface to volume ratio of Cut Cylindrical Shell formula is defined as ratio of surface area to volume of cut cylindrical shell is calculated using surface_to_volume_ratio = (Lateral Surface Area Polyhedron+(pi*((Radius 1^2)-(Radius^2)+(Radius 1*(sqrt((Radius 1^2)+(((Long outer height-Short outer height)/2)^2))))- (Radius*(sqrt((Radius^2)+(((Long inner height-Short inner height)/2)^2)))))))/((pi/2)*(((Radius 1^2)*(Short outer height+Long outer height))-((Radius^2)*(Short inner height+Long inner height)))). To calculate Surface to volume ratio of Cut Cylindrical Shell, you need Lateral Surface Area Polyhedron (SALateral_Polyhedron), Radius 1 (r1), Radius (r), Long outer height (hOuter_long), Short outer height (hOuter_short), Long inner height (hInner_long) & Short inner height (hInner_short). With our tool, you need to enter the respective value for Lateral Surface Area Polyhedron, Radius 1, Radius, Long outer height, Short outer height, Long inner height & Short inner height 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 Surface to Volume Ratio?
In this formula, Surface to Volume Ratio uses Lateral Surface Area Polyhedron, Radius 1, Radius, Long outer height, Short outer height, Long inner height & Short inner height. We can use 4 other way(s) to calculate the same, which is/are as follows -
  • surface_area_of_polyhedron = Lateral Surface Area Polyhedron+(pi*((Radius 1^2)-(Radius^2)+(Radius 1*(sqrt((Radius 1^2)+(((Long outer height-Short outer height)/2)^2))))- (Radius*(sqrt((Radius^2)+(((Long inner height-Short inner height)/2)^2))))))
  • volume_polyhedron = (pi/2)*(((Radius 1^2)*(Short outer height+Long outer height))-((Radius^2)*(Short inner height+Long inner height)))
  • surface_to_volume_ratio = (Lateral Surface Area Polyhedron+(pi*((Radius 1^2)-(Radius^2)+(Radius 1*(sqrt((Radius 1^2)+(((Long outer height-Short outer height)/2)^2))))- (Radius*(sqrt((Radius^2)+(((Long inner height-Short inner height)/2)^2)))))))/((pi/2)*(((Radius 1^2)*(Short outer height+Long outer height))-((Radius^2)*(Short inner height+Long inner height))))
  • surface_area_of_polyhedron = (pi*((Radius 1*(Short outer height+Long outer height))+(Radius*(Short inner height+Long inner height))))+(pi*((Radius 1^2)-(Radius^2)+(Radius 1*(sqrt((Radius 1^2)+(((Long outer height-Short outer height)/2)^2))))- (Radius*(sqrt((Radius^2)+(((Long inner height-Short inner height)/2)^2))))))
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