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

GoTotal Surface Area of Cylindrical Shell given Lateral Surface Area Formula

GoTotal Surface Area of Cylindrical Shell given Lateral Surface Area and Outer Radius Formula

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Total Surface Area of Cylindrical Shell is the total quantity of plane enclosed on the entire surface of the Cylindrical Shell. Check FAQs

TSA = 2 \cdot π \cdot (\sqrt{\frac{V}{π \cdot h} + {r Inner}^{2}} + r Inner) \cdot (\sqrt{\frac{V}{π \cdot h} + {r Inner}^{2}} - r Inner + h)

TSA - Total Surface Area of Cylindrical Shell?V - Volume of Cylindrical Shell?h - Height of Cylindrical Shell?r_Inner - Inner Radius of Cylindrical Shell?π - Archimedes' constant?

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

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Here is how the Total Surface Area of Cylindrical Shell given Volume and Inner Radius equation looks like.

853.9601 = 2 \cdot 3.1416 \cdot (\sqrt{\frac{800}{3.1416 \cdot 5} + 7^{2}} + 7) \cdot (\sqrt{\frac{800}{3.1416 \cdot 5} + 7^{2}} - 7 + 5)

853.9601m² = 2 \cdot 3.1416 \cdot (\sqrt{\frac{800m³}{3.1416 \cdot 5m} + {7m}^{2}} + 7m) \cdot (\sqrt{\frac{800m³}{3.1416 \cdot 5m} + {7m}^{2}} - 7m + 5m)

853.9601 = 2 \cdot 3.1416 \cdot (\sqrt{\frac{800}{3.1416 \cdot 5} + 7^{2}} + 7) \cdot (\sqrt{\frac{800}{3.1416 \cdot 5} + 7^{2}} - 7 + 5)

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

Follow our step by step solution on how to calculate Total Surface Area of Cylindrical Shell given Volume and Inner Radius?

FIRST Step Consider the formula

TSA = 2 \cdot π \cdot (\sqrt{\frac{V}{π \cdot h} + {r Inner}^{2}} + r Inner) \cdot (\sqrt{\frac{V}{π \cdot h} + {r Inner}^{2}} - r Inner + h)

Next Step Substitute values of Variables

∴

TSA = 2 \cdot π \cdot (\sqrt{\frac{800m³}{π \cdot 5m} + {7m}^{2}} + 7m) \cdot (\sqrt{\frac{800m³}{π \cdot 5m} + {7m}^{2}} - 7m + 5m)

Next Step Substitute values of Constants

∴

TSA = 2 \cdot 3.1416 \cdot (\sqrt{\frac{800m³}{3.1416 \cdot 5m} + {7m}^{2}} + 7m) \cdot (\sqrt{\frac{800m³}{3.1416 \cdot 5m} + {7m}^{2}} - 7m + 5m)

Next Step Prepare to Evaluate

∴

TSA = 2 \cdot 3.1416 \cdot (\sqrt{\frac{800}{3.1416 \cdot 5} + 7^{2}} + 7) \cdot (\sqrt{\frac{800}{3.1416 \cdot 5} + 7^{2}} - 7 + 5)

Next Step Evaluate

∴

TSA = 853.960118964001m²

LAST Step Rounding Answer

∴

TSA = 853.9601m²

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

Variables

Constants

Functions

Total Surface Area of Cylindrical Shell

Total Surface Area of Cylindrical Shell is the total quantity of plane enclosed on the entire surface of the Cylindrical Shell.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Cylindrical Shell

Volume of Cylindrical Shell

Volume of Cylindrical Shell is the total quantity of three dimensional space enclosed by the entire surface of the Cylindrical Shell.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Cylindrical Shell

Height of Cylindrical Shell

Height of Cylindrical Shell is the vertical distance from the base circular face to the top most point of the Cylindrical Shell.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Cylindrical Shell

Inner Radius of 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.

Symbol: r_Inner

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inner Radius of Cylindrical Shell

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sqrt(Number)

Other Formulas to find Total Surface Area of Cylindrical Shell

Go Total Surface Area of Cylindrical Shell given Lateral Surface Area

TSA = 2 \cdot π \cdot (r Outer + r Inner) \cdot (r Outer - r Inner + \frac{LSA}{2 \cdot π \cdot (r Outer + r Inner)})

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

TSA = \frac{LSA}{h} \cdot (r Outer - (\frac{LSA}{2 \cdot π \cdot h} - r Outer) + h)

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

TSA = \frac{LSA}{h} \cdot ((\frac{LSA}{2 \cdot π \cdot h} - r Inner) - r Inner + h)

Go Total Surface Area of Cylindrical Shell

TSA = 2 \cdot π \cdot (r Outer + r Inner) \cdot (r Outer - r Inner + h)

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

Total Surface Area of Cylindrical Shell given Volume and Inner Radius evaluator 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 evaluate 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 evaluate Total Surface Area of Cylindrical Shell given Volume and Inner Radius using this online evaluator? To use this online evaluator 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.

FAQs on Total Surface Area of Cylindrical Shell given Volume and Inner Radius

What is the formula to find Total Surface Area of Cylindrical Shell given Volume and Inner Radius?

The formula of Total Surface Area of Cylindrical Shell given Volume and Inner Radius is expressed as 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). Here is an example- 853.9601 = 2*pi*(sqrt(800/(pi*5)+7^2)+7)*(sqrt(800/(pi*5)+7^2)-7+5).

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

With Volume of Cylindrical Shell (V), Height of Cylindrical Shell (h) & Inner Radius of Cylindrical Shell (r_Inner) we can find Total Surface Area of Cylindrical Shell given Volume and Inner Radius using the formula - 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). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Total Surface Area of Cylindrical Shell?

Here are the different ways to Calculate Total Surface Area 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+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)

Can the Total Surface Area of Cylindrical Shell given Volume and Inner Radius be negative?

No, the Total Surface Area of Cylindrical Shell given Volume and Inner Radius, measured in Area cannot be negative.

Which unit is used to measure Total Surface Area of Cylindrical Shell given Volume and Inner Radius?

Total Surface Area of Cylindrical Shell given Volume and Inner Radius is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Total Surface Area of Cylindrical Shell given Volume and Inner Radius can be measured.

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

​GoTotal Surface Area of Cylindrical Shell given Lateral Surface Area Formula

​GoTotal Surface Area of Cylindrical Shell given Lateral Surface Area and Outer Radius Formula

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

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

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

Other Formulas to find Total Surface Area of Cylindrical Shell

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

FAQs on Total Surface Area of Cylindrical Shell given Volume and Inner Radius

Variable Name

GoTotal Surface Area of Cylindrical Shell given Lateral Surface Area Formula

GoTotal Surface Area of Cylindrical Shell given Lateral Surface Area and Outer Radius Formula