FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

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

GoTotal Surface Area of Cut Cylindrical Shell Formula

Fx Copy

LaTeX Copy

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

TSA = LSA + (π \cdot ({r Outer}^{2} - {r Inner}^{2} + (r Outer \cdot \sqrt{{r Outer}^{2} + {(\frac{h Long Outer - h Short Outer}{2})}^{2}}) - (r Inner \cdot \sqrt{{r Inner}^{2} + {(\frac{h Long Inner - h Short Inner}{2})}^{2}})))

TSA - Total Surface Area of Cut Cylindrical Shell?LSA - Lateral Surface Area of Cut Cylindrical Shell?r_Outer - Outer Radius of Cut Cylindrical Shell?r_Inner - Inner Radius of Cut Cylindrical Shell?h_{Long Outer} - Long Outer Height of Cut Cylindrical Shell?h_{Short Outer} - Short Outer Height of Cut Cylindrical Shell?h_{Long Inner} - Long Inner Height of Cut Cylindrical Shell?h_{Short Inner} - Short Inner Height of Cut Cylindrical Shell?π - Archimedes' constant?

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

With values

With units

Only example

Here is how the Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area equation looks like with Values.

Here is how the Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area equation looks like with Units.

Here is how the Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area equation looks like.

2807.3303 = 2300 + (3.1416 \cdot (12^{2} - 8^{2} + (12 \cdot \sqrt{12^{2} + {(\frac{20 - 16}{2})}^{2}}) - (8 \cdot \sqrt{8^{2} + {(\frac{19 - 17}{2})}^{2}})))

2807.3303m² = 2300m² + (3.1416 \cdot ({12m}^{2} - {8m}^{2} + (12m \cdot \sqrt{{12m}^{2} + {(\frac{20m - 16m}{2})}^{2}}) - (8m \cdot \sqrt{{8m}^{2} + {(\frac{19m - 17m}{2})}^{2}})))

2807.3303 = 2300 + (3.1416 \cdot (12^{2} - 8^{2} + (12 \cdot \sqrt{12^{2} + {(\frac{20 - 16}{2})}^{2}}) - (8 \cdot \sqrt{8^{2} + {(\frac{19 - 17}{2})}^{2}})))

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Math » Category

Geometry » Category

3D Geometry » fx Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area

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

Follow our step by step solution on how to calculate Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area?

FIRST Step Consider the formula

TSA = LSA + (π \cdot ({r Outer}^{2} - {r Inner}^{2} + (r Outer \cdot \sqrt{{r Outer}^{2} + {(\frac{h Long Outer - h Short Outer}{2})}^{2}}) - (r Inner \cdot \sqrt{{r Inner}^{2} + {(\frac{h Long Inner - h Short Inner}{2})}^{2}})))

Next Step Substitute values of Variables

∴

TSA = 2300m² + (π \cdot ({12m}^{2} - {8m}^{2} + (12m \cdot \sqrt{{12m}^{2} + {(\frac{20m - 16m}{2})}^{2}}) - (8m \cdot \sqrt{{8m}^{2} + {(\frac{19m - 17m}{2})}^{2}})))

Next Step Substitute values of Constants

∴

TSA = 2300m² + (3.1416 \cdot ({12m}^{2} - {8m}^{2} + (12m \cdot \sqrt{{12m}^{2} + {(\frac{20m - 16m}{2})}^{2}}) - (8m \cdot \sqrt{{8m}^{2} + {(\frac{19m - 17m}{2})}^{2}})))

Next Step Prepare to Evaluate

∴

TSA = 2300 + (3.1416 \cdot (12^{2} - 8^{2} + (12 \cdot \sqrt{12^{2} + {(\frac{20 - 16}{2})}^{2}}) - (8 \cdot \sqrt{8^{2} + {(\frac{19 - 17}{2})}^{2}})))

Next Step Evaluate

∴

TSA = 2807.33026446915m²

LAST Step Rounding Answer

∴

TSA = 2807.3303m²

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

Variables

Constants

Functions

Total Surface Area of Cut Cylindrical Shell

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

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Cut Cylindrical Shell

Lateral Surface Area of Cut Cylindrical Shell

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.

Symbol: LSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Lateral Surface Area of Cut Cylindrical Shell

Outer Radius of 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.

Symbol: r_Outer

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Outer Radius of Cut Cylindrical Shell

Inner Radius of 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.

Symbol: r_Inner

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inner Radius of Cut Cylindrical Shell

Long Outer Height of 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.

Symbol: h_{Long Outer}

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Long Outer Height of Cut Cylindrical Shell

Short Outer Height of 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.

Symbol: h_{Short Outer}

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Short Outer Height of Cut Cylindrical Shell

Long Inner Height of 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.

Symbol: h_{Long Inner}

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Long Inner Height of Cut Cylindrical Shell

Short Inner Height of 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.

Symbol: h_{Short Inner}

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Short Inner Height of Cut 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 Cut Cylindrical Shell

Go Total Surface Area of Cut Cylindrical Shell

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

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

Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area evaluator 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 evaluate 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 evaluate Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area using this online evaluator? To use this online evaluator 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.

FAQs on Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area

What is the formula to find Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area?

The formula of Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area is expressed as 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)))). Here is an example- 2807.33 = 2300+(pi*(12^2-8^2+(12*sqrt(12^2+((20-16)/2)^2))-(8*sqrt(8^2+((19-17)/2)^2)))).

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

With 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}) we can find Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area using the formula - 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)))). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

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

Here are the different ways to Calculate Total Surface Area of Cut Cylindrical Shell-

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))))

Can the Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area be negative?

No, the Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area, measured in Area cannot be negative.

Which unit is used to measure Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area?

Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area 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 Cut Cylindrical Shell given Lateral Surface Area can be measured.

Let Others Know

✖

Facebook

Twitter

Copied!

: Value
: Unit

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

​GoTotal Surface Area of Cut Cylindrical Shell Formula

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

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

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

Other Formulas to find Total Surface Area of Cut Cylindrical Shell

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

FAQs on Total Surface Area of Cut Cylindrical Shell given Lateral Surface Area

Variable Name

GoTotal Surface Area of Cut Cylindrical Shell Formula