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Total Surface Area of Pentagonal Cupola given Height Formula

GoTotal Surface Area of Pentagonal Cupola Formula

GoTotal Surface Area of Pentagonal Cupola given Volume Formula

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Total Surface Area of Pentagonal Cupola is the total amount of 2D space occupied by all the faces of the Pentagonal Cupola. Check FAQs

TSA = \frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))}) \cdot (\frac{h^{2}}{1 - (\frac{1}{4} \cdot \cos e c {(\frac{π}{5})}^{2})})

TSA - Total Surface Area of Pentagonal Cupola?h - Height of Pentagonal Cupola?π - Archimedes' constant?

Total Surface Area of Pentagonal Cupola given Height Example

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Here is how the Total Surface Area of Pentagonal Cupola given Height equation looks like with Values.

Here is how the Total Surface Area of Pentagonal Cupola given Height equation looks like with Units.

Here is how the Total Surface Area of Pentagonal Cupola given Height equation looks like.

1499.6525 = \frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))}) \cdot (\frac{5^{2}}{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{5})}^{2})})

1499.6525m² = \frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))}) \cdot (\frac{{5m}^{2}}{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{5})}^{2})})

1499.6525 = \frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))}) \cdot (\frac{5^{2}}{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{5})}^{2})})

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Total Surface Area of Pentagonal Cupola given Height Solution

Follow our step by step solution on how to calculate Total Surface Area of Pentagonal Cupola given Height?

FIRST Step Consider the formula

TSA = \frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))}) \cdot (\frac{h^{2}}{1 - (\frac{1}{4} \cdot \cos e c {(\frac{π}{5})}^{2})})

Next Step Substitute values of Variables

∴

TSA = \frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))}) \cdot (\frac{{5m}^{2}}{1 - (\frac{1}{4} \cdot \cos e c {(\frac{π}{5})}^{2})})

Next Step Substitute values of Constants

∴

TSA = \frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))}) \cdot (\frac{{5m}^{2}}{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{5})}^{2})})

Next Step Prepare to Evaluate

∴

TSA = \frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))}) \cdot (\frac{5^{2}}{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{5})}^{2})})

Next Step Evaluate

∴

TSA = 1499.65245328197m²

LAST Step Rounding Answer

∴

TSA = 1499.6525m²

Total Surface Area of Pentagonal Cupola given Height Formula Elements

Variables

Constants

Functions

Total Surface Area of Pentagonal Cupola

Total Surface Area of Pentagonal Cupola is the total amount of 2D space occupied by all the faces of the Pentagonal Cupola.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Pentagonal Cupola

Height of Pentagonal Cupola

Height of Pentagonal Cupola is the vertical distance from the pentagonal face to the opposite decagonal face of the Pentagonal Cupola.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Pentagonal Cupola

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

sec

Secant is a trigonometric function that is defined ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine.

Syntax: sec(Angle)

cosec

The cosecant function is a trigonometric function that is the reciprocal of the sine function.

Syntax: cosec(Angle)

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 Pentagonal Cupola

Go Total Surface Area of Pentagonal Cupola

TSA = \frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))}) \cdot {l e}^{2}

Go Total Surface Area of Pentagonal Cupola given Volume

TSA = \frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))}) \cdot {(\frac{V}{\frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5}))})}^{\frac{2}{3}}

Go Total Surface Area of Pentagonal Cupola given Surface to Volume Ratio

TSA = \frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))}) \cdot {(\frac{\frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))})}{\frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5})) \cdot R A/V})}^{2}

How to Evaluate Total Surface Area of Pentagonal Cupola given Height?

Total Surface Area of Pentagonal Cupola given Height evaluator uses Total Surface Area of Pentagonal Cupola = 1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5)))))*(Height of Pentagonal Cupola^(2)/(1-(1/4*cosec(pi/5)^(2)))) to evaluate the Total Surface Area of Pentagonal Cupola, The Total Surface Area of Pentagonal Cupola given Height formula is defined as the total amount of two-dimensional space occupied by all the faces of the Pentagonal Cupola and is calculated using the height of the Pentagonal Cupola. Total Surface Area of Pentagonal Cupola is denoted by TSA symbol.

How to evaluate Total Surface Area of Pentagonal Cupola given Height using this online evaluator? To use this online evaluator for Total Surface Area of Pentagonal Cupola given Height, enter Height of Pentagonal Cupola (h) and hit the calculate button.

FAQs on Total Surface Area of Pentagonal Cupola given Height

What is the formula to find Total Surface Area of Pentagonal Cupola given Height?

The formula of Total Surface Area of Pentagonal Cupola given Height is expressed as Total Surface Area of Pentagonal Cupola = 1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5)))))*(Height of Pentagonal Cupola^(2)/(1-(1/4*cosec(pi/5)^(2)))). Here is an example- 1499.652 = 1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5)))))*(5^(2)/(1-(1/4*cosec(pi/5)^(2)))).

How to calculate Total Surface Area of Pentagonal Cupola given Height?

With Height of Pentagonal Cupola (h) we can find Total Surface Area of Pentagonal Cupola given Height using the formula - Total Surface Area of Pentagonal Cupola = 1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5)))))*(Height of Pentagonal Cupola^(2)/(1-(1/4*cosec(pi/5)^(2)))). This formula also uses Archimedes' constant and , Secant Function, cosecant , Square Root Function function(s).

What are the other ways to Calculate Total Surface Area of Pentagonal Cupola?

Here are the different ways to Calculate Total Surface Area of Pentagonal Cupola-

Total Surface Area of Pentagonal Cupola=1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5)))))*Edge Length of Pentagonal Cupola^2
Total Surface Area of Pentagonal Cupola=1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5)))))*(Volume of Pentagonal Cupola/(1/6*(5+(4*sqrt(5)))))^(2/3)
Total Surface Area of Pentagonal Cupola=1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5)))))*((1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*Surface to Volume Ratio of Pentagonal Cupola))^2

Can the Total Surface Area of Pentagonal Cupola given Height be negative?

No, the Total Surface Area of Pentagonal Cupola given Height, measured in Area cannot be negative.

Which unit is used to measure Total Surface Area of Pentagonal Cupola given Height?

Total Surface Area of Pentagonal Cupola given Height 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 Pentagonal Cupola given Height can be measured.

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