Total Surface Area of Cylindrical Shell given Volume and Inner Radius Calculator

✖Volume of Cylindrical Shell is the total quantity of three dimensional space enclosed by the entire surface of the Cylindrical Shell.ⓘ Volume of Cylindrical Shell [V]			+10% -10%
✖Height of Cylindrical Shell is the vertical distance from the base circular face to the top most point of the Cylindrical Shell.ⓘ Height of Cylindrical Shell [h]			+10% -10%
✖Inner Radius of Cylindrical Shell is the distance between center and any point on the circumference of any of the circular faces in the inner cylinder of the Cylindrical Shell.ⓘ Inner Radius of Cylindrical Shell [r_Inner]			+10% -10%

✖Total Surface Area of Cylindrical Shell is the total quantity of plane enclosed on the entire surface of the Cylindrical Shell.ⓘ Total Surface Area of Cylindrical Shell given Volume and Inner Radius [TSA]

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Formula

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Total Surface Area of Cylindrical Shell given Volume and Inner Radius

Formula

`"TSA" = 2*pi*(sqrt("V"/(pi*"h")+"r"_{"Inner"}^2)+"r"_{"Inner"})*(sqrt("V"/(pi*"h")+"r"_{"Inner"}^2)-"r"_{"Inner"}+"h")`

Example

`"853.9601m²"=2*pi*(sqrt("800m³"/(pi*"5m")+("7m")^2)+"7m")*(sqrt("800m³"/(pi*"5m")+("7m")^2)-"7m"+"5m")`

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Total Surface Area of Cylindrical Shell given Volume and Inner Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Cylindrical Shell = 2*pi*(sqrt(Volume of Cylindrical Shell/(pi*Height of Cylindrical Shell)+Inner Radius of Cylindrical Shell^2)+Inner Radius of Cylindrical Shell)*(sqrt(Volume of Cylindrical Shell/(pi*Height of Cylindrical Shell)+Inner Radius of Cylindrical Shell^2)-Inner Radius of Cylindrical Shell+Height of Cylindrical Shell)
TSA = 2*pi*(sqrt(V/(pi*h)+r_Inner^2)+r_Inner)*(sqrt(V/(pi*h)+r_Inner^2)-r_Inner+h)
This formula uses 1 Constants, 1 Functions, 4 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 Cylindrical Shell - (Measured in Square Meter) - Total Surface Area of Cylindrical Shell is the total quantity of plane enclosed on the entire surface of the Cylindrical Shell.
Volume of Cylindrical Shell - (Measured in Cubic Meter) - Volume of Cylindrical Shell is the total quantity of three dimensional space enclosed by the entire surface of the Cylindrical Shell.
Height of Cylindrical Shell - (Measured in Meter) - Height of Cylindrical Shell is the vertical distance from the base circular face to the top most point of the Cylindrical Shell.
Inner Radius of Cylindrical Shell - (Measured in Meter) - Inner Radius of Cylindrical Shell is the distance between center and any point on the circumference of any of the circular faces in the inner cylinder of the Cylindrical Shell.

STEP 1: Convert Input(s) to Base Unit

Volume of Cylindrical Shell: 800 Cubic Meter --> 800 Cubic Meter No Conversion Required
Height of Cylindrical Shell: 5 Meter --> 5 Meter No Conversion Required
Inner Radius of Cylindrical Shell: 7 Meter --> 7 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = 2*pi*(sqrt(V/(pi*h)+r_Inner^2)+r_Inner)*(sqrt(V/(pi*h)+r_Inner^2)-r_Inner+h) --> 2*pi*(sqrt(800/(pi*5)+7^2)+7)*(sqrt(800/(pi*5)+7^2)-7+5)

Evaluating ... ...

TSA = 853.960118964001

STEP 3: Convert Result to Output's Unit

853.960118964001 Square Meter --> No Conversion Required

FINAL ANSWER

853.960118964001 ≈ 853.9601 Square Meter <-- Total Surface Area of Cylindrical Shell

(Calculation completed in 00.004 seconds)

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< 8 Total Surface Area of Cylindrical Shell Calculators

Total Surface Area of Cylindrical Shell given Volume and Inner Radius

Go Total Surface Area of Cylindrical Shell = 2*pi*(sqrt(Volume of Cylindrical Shell/(pi*Height of Cylindrical Shell)+Inner Radius of Cylindrical Shell^2)+Inner Radius of Cylindrical Shell)*(sqrt(Volume of Cylindrical Shell/(pi*Height of Cylindrical Shell)+Inner Radius of Cylindrical Shell^2)-Inner Radius of Cylindrical Shell+Height of Cylindrical Shell)

Total Surface Area of Cylindrical Shell given Lateral Surface Area

Go Total Surface Area of Cylindrical Shell = 2*pi*(Outer Radius of Cylindrical Shell+Inner Radius of Cylindrical Shell)*(Outer Radius of Cylindrical Shell-Inner Radius of Cylindrical Shell+Lateral Surface Area of Cylindrical Shell/(2*pi*(Outer Radius of Cylindrical Shell+Inner Radius of Cylindrical Shell)))

Total Surface Area of Cylindrical Shell given Volume

Go Total Surface Area of Cylindrical Shell = 2*pi*(Outer Radius of Cylindrical Shell+Inner Radius of Cylindrical Shell)*(Outer Radius of Cylindrical Shell-Inner Radius of Cylindrical Shell+Volume of Cylindrical Shell/(pi*(Outer Radius of Cylindrical Shell^2-Inner Radius of Cylindrical Shell^2)))

Total Surface Area of Cylindrical Shell given Wall Thickness and Inner Radius

Go Total Surface Area of Cylindrical Shell = 2*pi*((Wall Thickness of Cylindrical Shell+Inner Radius of Cylindrical Shell)+Inner Radius of Cylindrical Shell)*((Wall Thickness of Cylindrical Shell+Inner Radius of Cylindrical Shell)-Inner Radius of Cylindrical Shell+Height of Cylindrical Shell)

Total Surface Area of Cylindrical Shell given Lateral Surface Area and Outer Radius

Go Total Surface Area of Cylindrical Shell = Lateral Surface Area of Cylindrical Shell/Height of Cylindrical Shell*(Outer Radius of Cylindrical Shell-(Lateral Surface Area of Cylindrical Shell/(2*pi*Height of Cylindrical Shell)-Outer Radius of Cylindrical Shell)+Height of Cylindrical Shell)

Total Surface Area of Cylindrical Shell given Lateral Surface Area and Inner Radius

Go Total Surface Area of Cylindrical Shell = Lateral Surface Area of Cylindrical Shell/Height of Cylindrical Shell*((Lateral Surface Area of Cylindrical Shell/(2*pi*Height of Cylindrical Shell)-Inner Radius of Cylindrical Shell)-Inner Radius of Cylindrical Shell+Height of Cylindrical Shell)

Total Surface Area of Cylindrical Shell

Total Surface Area of Cylindrical Shell given Wall Thickness and Outer Radius

Go Total Surface Area of Cylindrical Shell = 2*pi*((2*Outer Radius of Cylindrical Shell)-Wall Thickness of Cylindrical Shell)*(Wall Thickness of Cylindrical Shell+Height of Cylindrical Shell)

Total Surface Area of Cylindrical Shell given Volume and Inner Radius Formula

What is a Cylindrical Shell?

A Cylindrical Shell is simply speaking, the space enclosed by two concentric circular cylinders. That is, if two circular cylinders of same height are kept one inside another, in such a way that their central axis coincide, then the space bounded in between these cylinders along with the annulus surfaces of proper size on the top and bottom together forms the Cylindrical Shell. An annulus in two dimensions is the compression of a Cylindrical Shell into a horizontal plane.

How to Calculate Total Surface Area of Cylindrical Shell given Volume and Inner Radius?

Total Surface Area of Cylindrical Shell given Volume and Inner Radius calculator uses Total Surface Area of Cylindrical Shell = 2*pi*(sqrt(Volume of Cylindrical Shell/(pi*Height of Cylindrical Shell)+Inner Radius of Cylindrical Shell^2)+Inner Radius of Cylindrical Shell)*(sqrt(Volume of Cylindrical Shell/(pi*Height of Cylindrical Shell)+Inner Radius of Cylindrical Shell^2)-Inner Radius of Cylindrical Shell+Height of Cylindrical Shell) to calculate the Total Surface Area of Cylindrical Shell, Total Surface Area of Cylindrical Shell given Volume and Inner Radius formula is defined as the total quantity of plane enclosed on the entire surface of the Cylindrical Shell, and calculated using the volume and inner radius of the Cylindrical Shell. Total Surface Area of Cylindrical Shell is denoted by TSA symbol.

How to calculate Total Surface Area of Cylindrical Shell given Volume and Inner Radius using this online calculator? To use this online calculator for Total Surface Area of Cylindrical Shell given Volume and Inner Radius, enter Volume of Cylindrical Shell (V), Height of Cylindrical Shell (h) & Inner Radius of Cylindrical Shell (r_Inner) and hit the calculate button. Here is how the Total Surface Area of Cylindrical Shell given Volume and Inner Radius calculation can be explained with given input values -> 853.9601 = 2*pi*(sqrt(800/(pi*5)+7^2)+7)*(sqrt(800/(pi*5)+7^2)-7+5).

FAQ

What is Total Surface Area of Cylindrical Shell given Volume and Inner Radius?

Total Surface Area of Cylindrical Shell given Volume and Inner Radius formula is defined as the total quantity of plane enclosed on the entire surface of the Cylindrical Shell, and calculated using the volume and inner radius of the Cylindrical Shell and is represented as TSA = 2*pi*(sqrt(V/(pi*h)+r_Inner^2)+r_Inner)*(sqrt(V/(pi*h)+r_Inner^2)-r_Inner+h) or Total Surface Area of Cylindrical Shell = 2*pi*(sqrt(Volume of Cylindrical Shell/(pi*Height of Cylindrical Shell)+Inner Radius of Cylindrical Shell^2)+Inner Radius of Cylindrical Shell)*(sqrt(Volume of Cylindrical Shell/(pi*Height of Cylindrical Shell)+Inner Radius of Cylindrical Shell^2)-Inner Radius of Cylindrical Shell+Height of Cylindrical Shell). Volume of Cylindrical Shell is the total quantity of three dimensional space enclosed by the entire surface of the Cylindrical Shell, Height of Cylindrical Shell is the vertical distance from the base circular face to the top most point of the Cylindrical Shell & Inner Radius of Cylindrical Shell is the distance between center and any point on the circumference of any of the circular faces in the inner cylinder of the Cylindrical Shell.

How to calculate Total Surface Area of Cylindrical Shell given Volume and Inner Radius?

Total Surface Area of Cylindrical Shell given Volume and Inner Radius formula is defined as the total quantity of plane enclosed on the entire surface of the Cylindrical Shell, and calculated using the volume and inner radius of the Cylindrical Shell is calculated using Total Surface Area of Cylindrical Shell = 2*pi*(sqrt(Volume of Cylindrical Shell/(pi*Height of Cylindrical Shell)+Inner Radius of Cylindrical Shell^2)+Inner Radius of Cylindrical Shell)*(sqrt(Volume of Cylindrical Shell/(pi*Height of Cylindrical Shell)+Inner Radius of Cylindrical Shell^2)-Inner Radius of Cylindrical Shell+Height of Cylindrical Shell). To calculate Total Surface Area of Cylindrical Shell given Volume and Inner Radius, you need Volume of Cylindrical Shell (V), Height of Cylindrical Shell (h) & Inner Radius of Cylindrical Shell (r_Inner). With our tool, you need to enter the respective value for Volume of Cylindrical Shell, Height of Cylindrical Shell & Inner Radius of 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 Cylindrical Shell?

In this formula, Total Surface Area of Cylindrical Shell uses Volume of Cylindrical Shell, Height of Cylindrical Shell & Inner Radius of Cylindrical Shell. We can use 7 other way(s) to calculate the same, which is/are as follows -

Total Surface Area of Cylindrical Shell = 2*pi*(Outer Radius of Cylindrical Shell+Inner Radius of Cylindrical Shell)*(Outer Radius of Cylindrical Shell-Inner Radius of Cylindrical Shell+Lateral Surface Area of Cylindrical Shell/(2*pi*(Outer Radius of Cylindrical Shell+Inner Radius of Cylindrical Shell)))
Total Surface Area of Cylindrical Shell = Lateral Surface Area of Cylindrical Shell/Height of Cylindrical Shell*(Outer Radius of Cylindrical Shell-(Lateral Surface Area of Cylindrical Shell/(2*pi*Height of Cylindrical Shell)-Outer Radius of Cylindrical Shell)+Height of Cylindrical Shell)
Total Surface Area of Cylindrical Shell = Lateral Surface Area of Cylindrical Shell/Height of Cylindrical Shell*((Lateral Surface Area of Cylindrical Shell/(2*pi*Height of Cylindrical Shell)-Inner Radius of Cylindrical Shell)-Inner Radius of Cylindrical Shell+Height of Cylindrical Shell)
Total Surface Area of Cylindrical Shell = 2*pi*(Outer Radius of Cylindrical Shell+Inner Radius of Cylindrical Shell)*(Outer Radius of Cylindrical Shell-Inner Radius of Cylindrical Shell+Height of Cylindrical Shell)
Total Surface Area of Cylindrical Shell = 2*pi*(Outer Radius of Cylindrical Shell+Inner Radius of Cylindrical Shell)*(Outer Radius of Cylindrical Shell-Inner Radius of Cylindrical Shell+Volume of Cylindrical Shell/(pi*(Outer Radius of Cylindrical Shell^2-Inner Radius of Cylindrical Shell^2)))
Total Surface Area of Cylindrical Shell = 2*pi*((2*Outer Radius of Cylindrical Shell)-Wall Thickness of Cylindrical Shell)*(Wall Thickness of Cylindrical Shell+Height of Cylindrical Shell)
Total Surface Area of Cylindrical Shell = 2*pi*((Wall Thickness of Cylindrical Shell+Inner Radius of Cylindrical Shell)+Inner Radius of Cylindrical Shell)*((Wall Thickness of Cylindrical Shell+Inner Radius of Cylindrical Shell)-Inner Radius of Cylindrical Shell+Height of Cylindrical Shell)

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