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Surface area of Cut Cylindrical Shell Solution

STEP 0: Pre-Calculation Summary
Formula Used
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))))))
SAPolyhedron = 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))))))
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
SAPolyhedron = 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)))))) --> 2000+(pi*((11^2)-(10^2)+(11*(sqrt((11^2)+(((16-12)/2)^2))))- (10*(sqrt((10^2)+(((15.9-12.1)/2)^2))))))
Evaluating ... ...
SAPolyhedron = 2132.55868935639
STEP 3: Convert Result to Output's Unit
2132.55868935639 Square Meter --> No Conversion Required
FINAL ANSWER
2132.55868935639 Square Meter <-- Surface area of Polyhedron
(Calculation completed in 00.031 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 area of Cut Cylindrical Shell Formula

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))))))
SAPolyhedron = 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))))))

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 area of Cut Cylindrical Shell?

Surface area of Cut Cylindrical Shell calculator uses 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)))))) to calculate the Surface area of Polyhedron, The Surface area of Cut Cylindrical Shell formula is defined as a measure of the total area that the surface of the Cut Cylindrical Shell occupies. Where, radius_1 = radius of outer cylinder and radius = radius of inner cylinder. Surface area of Polyhedron is denoted by SAPolyhedron symbol.

How to calculate Surface area of Cut Cylindrical Shell using this online calculator? To use this online calculator for Surface area 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 area of Cut Cylindrical Shell calculation can be explained with given input values -> 2132.559 = 2000+(pi*((11^2)-(10^2)+(11*(sqrt((11^2)+(((16-12)/2)^2))))- (10*(sqrt((10^2)+(((15.9-12.1)/2)^2)))))).

FAQ

What is Surface area of Cut Cylindrical Shell?
The Surface area of Cut Cylindrical Shell formula is defined as a measure of the total area that the surface of the Cut Cylindrical Shell occupies. Where, radius_1 = radius of outer cylinder and radius = radius of inner cylinder and is represented as SAPolyhedron = 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)))))) or 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)))))). 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 area of Cut Cylindrical Shell?
The Surface area of Cut Cylindrical Shell formula is defined as a measure of the total area that the surface of the Cut Cylindrical Shell occupies. Where, radius_1 = radius of outer cylinder and radius = radius of inner cylinder is calculated using 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)))))). To calculate Surface area 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 area of Polyhedron?
In this formula, Surface area of Polyhedron 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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