Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area Calculator

✖Lateral Surface Area of Cut Cylindrical Shell is the total quantity of plane enclosed on all the lateral curved surfaces ( that is, top and bottom faces are excluded) of the Cut Cylindrical Shell.ⓘ Lateral Surface Area of Cut Cylindrical Shell [LSA]			+10% -10%
✖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%
✖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%
✖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%
✖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 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%
✖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%

✖Total Surface Area of Cut Cylindrical Shell is the total quantity of plane enclosed on the entire surface of the Cut Cylindrical Shell.ⓘ Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area [TSA]

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Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Cut Cylindrical Shell = Lateral Surface Area 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))))
TSA = LSA+(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))))
This formula uses 1 Constants, 1 Functions, 8 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

Total Surface Area of Cut Cylindrical Shell - (Measured in Square Meter) - Total Surface Area of Cut Cylindrical Shell is the total quantity of plane enclosed on the entire surface of the Cut Cylindrical Shell.
Lateral Surface Area of Cut Cylindrical Shell - (Measured in Square Meter) - Lateral Surface Area of Cut Cylindrical Shell is the total quantity of plane enclosed on all the lateral curved surfaces ( that is, top and bottom faces are excluded) 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.
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.
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.
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 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.
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.

STEP 1: Convert Input(s) to Base Unit

Lateral Surface Area of Cut Cylindrical Shell: 2300 Square Meter --> 2300 Square Meter No Conversion Required
Outer Radius of Cut Cylindrical Shell: 12 Meter --> 12 Meter No Conversion Required
Inner Radius of Cut Cylindrical Shell: 8 Meter --> 8 Meter No Conversion Required
Long Outer Height of Cut Cylindrical Shell: 20 Meter --> 20 Meter No Conversion Required
Short Outer Height of Cut Cylindrical Shell: 16 Meter --> 16 Meter No Conversion Required
Long Inner Height of Cut Cylindrical Shell: 19 Meter --> 19 Meter No Conversion Required
Short Inner Height of Cut Cylindrical Shell: 17 Meter --> 17 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = LSA+(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)))) --> 2300+(pi*(12^2-8^2+(12*sqrt(12^2+((20-16)/2)^2))-(8*sqrt(8^2+((19-17)/2)^2))))

Evaluating ... ...

TSA = 2807.33026446915

STEP 3: Convert Result to Output's Unit

2807.33026446915 Square Meter --> No Conversion Required

FINAL ANSWER

2807.33026446915 ≈ 2807.33 Square Meter <-- Total Surface Area of Cut Cylindrical Shell

(Calculation completed in 00.008 seconds)

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< Total Surface Area of Cut Cylindrical Shell Calculators

Total Surface Area of Cut Cylindrical Shell

LaTeX Go Total Surface Area 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))))

Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area

LaTeX Go Total Surface Area of Cut Cylindrical Shell = Lateral Surface Area 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))))

Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area Formula

LaTeX Go

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 Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area?

Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area calculator uses Total Surface Area of Cut Cylindrical Shell = Lateral Surface Area 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)))) to calculate the Total Surface Area of Cut Cylindrical Shell, Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area formula is defined as the total quantity of plane enclosed on the entire surface of the Cut Cylindrical Shell, and calculated using outer radius, outer height, inner radius, inner height and lateral surface area of the Cut Cylindrical Shell. Total Surface Area of Cut Cylindrical Shell is denoted by TSA symbol.

How to calculate Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area using this online calculator? To use this online calculator for Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area, enter Lateral Surface Area of Cut Cylindrical Shell (LSA), Outer Radius of Cut Cylindrical Shell (r_Outer), Inner Radius of Cut Cylindrical Shell (r_Inner), Long Outer Height of Cut Cylindrical Shell (h_{Long Outer}), Short Outer Height of Cut Cylindrical Shell (h_{Short Outer}), Long Inner Height of Cut Cylindrical Shell (h_{Long Inner}) & Short Inner Height of Cut Cylindrical Shell (h_{Short Inner}) and hit the calculate button. Here is how the Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area calculation can be explained with given input values -> 2807.33 = 2300+(pi*(12^2-8^2+(12*sqrt(12^2+((20-16)/2)^2))-(8*sqrt(8^2+((19-17)/2)^2)))).

FAQ

What is Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area?

Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area formula is defined as the total quantity of plane enclosed on the entire surface of the Cut Cylindrical Shell, and calculated using outer radius, outer height, inner radius, inner height and lateral surface area of the Cut Cylindrical Shell and is represented as TSA = LSA+(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)))) or Total Surface Area of Cut Cylindrical Shell = Lateral Surface Area 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)))). Lateral Surface Area of Cut Cylindrical Shell is the total quantity of plane enclosed on all the lateral curved surfaces ( that is, top and bottom faces are excluded) of the 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, 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, 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, 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 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 & 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.

How to calculate Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area?

Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area formula is defined as the total quantity of plane enclosed on the entire surface of the Cut Cylindrical Shell, and calculated using outer radius, outer height, inner radius, inner height and lateral surface area of the Cut Cylindrical Shell is calculated using Total Surface Area of Cut Cylindrical Shell = Lateral Surface Area 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)))). To calculate Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area, you need Lateral Surface Area of Cut Cylindrical Shell (LSA), Outer Radius of Cut Cylindrical Shell (r_Outer), Inner Radius of Cut Cylindrical Shell (r_Inner), Long Outer Height of Cut Cylindrical Shell (h_{Long Outer}), Short Outer Height of Cut Cylindrical Shell (h_{Short Outer}), Long Inner Height of Cut Cylindrical Shell (h_{Long Inner}) & Short Inner Height of Cut Cylindrical Shell (h_{Short Inner}). With our tool, you need to enter the respective value for Lateral Surface Area of Cut Cylindrical Shell, Outer Radius of Cut Cylindrical Shell, Inner Radius of Cut Cylindrical Shell, Long Outer Height of Cut Cylindrical Shell, Short Outer Height of Cut Cylindrical Shell, Long Inner Height of Cut Cylindrical Shell & Short 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.

How many ways are there to calculate Total Surface Area of Cut Cylindrical Shell?

In this formula, Total Surface Area of Cut Cylindrical Shell uses Lateral Surface Area of Cut Cylindrical Shell, Outer Radius of Cut Cylindrical Shell, Inner Radius of Cut Cylindrical Shell, Long Outer Height of Cut Cylindrical Shell, Short Outer Height of Cut Cylindrical Shell, Long Inner Height of Cut Cylindrical Shell & Short Inner Height of Cut Cylindrical Shell. We can use 1 other way(s) to calculate the same, which is/are as follows -

Total Surface Area 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))))

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