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Height of Pentagonal Cupola given Total Surface Area Formula

GoHeight of Pentagonal Cupola Formula

GoHeight of Pentagonal Cupola given Volume Formula

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

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

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

Height of Pentagonal Cupola given Total Surface Area Example

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

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

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

5.2605 = \sqrt{\frac{1660}{\frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))})}} \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{5})}^{2})}

5.2605m = \sqrt{\frac{1660m²}{\frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))})}} \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{5})}^{2})}

5.2605 = \sqrt{\frac{1660}{\frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))})}} \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{5})}^{2})}

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Height of Pentagonal Cupola given Total Surface Area Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

h = \sqrt{\frac{1660m²}{\frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))})}} \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{π}{5})}^{2})}

Next Step Substitute values of Constants

∴

h = \sqrt{\frac{1660m²}{\frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))})}} \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{5})}^{2})}

Next Step Prepare to Evaluate

∴

h = \sqrt{\frac{1660}{\frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))})}} \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{5})}^{2})}

Next Step Evaluate

∴

h = 5.26052074023069m

LAST Step Rounding Answer

∴

h = 5.2605m

Height of Pentagonal Cupola given Total Surface Area Formula Elements

Variables

Constants

Functions

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

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

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 Height of Pentagonal Cupola

Go Height of Pentagonal Cupola

h = l e \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{π}{5})}^{2})}

Go Height of Pentagonal Cupola given Volume

h = {(\frac{V}{\frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5}))})}^{\frac{1}{3}} \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{π}{5})}^{2})}

Go Height of Pentagonal Cupola given Surface to Volume Ratio

h = \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} \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{π}{5})}^{2})}

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

Height of Pentagonal Cupola given Total Surface Area evaluator uses Height of Pentagonal Cupola = sqrt(Total Surface Area of Pentagonal Cupola/(1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5)))))))*sqrt(1-(1/4*cosec(pi/5)^(2))) to evaluate the Height of Pentagonal Cupola, The Height of Pentagonal Cupola given Total Surface Area formula is defined as the vertical distance from the pentagonal face to the opposite decagonal face of the Pentagonal Cupola and is calculated using the total surface area of the Pentagonal Cupola. Height of Pentagonal Cupola is denoted by h symbol.

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

FAQs on Height of Pentagonal Cupola given Total Surface Area

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

The formula of Height of Pentagonal Cupola given Total Surface Area is expressed as Height of Pentagonal Cupola = sqrt(Total Surface Area of Pentagonal Cupola/(1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5)))))))*sqrt(1-(1/4*cosec(pi/5)^(2))). Here is an example- 5.260521 = sqrt(1660/(1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5)))))))*sqrt(1-(1/4*cosec(pi/5)^(2))).

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

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

What are the other ways to Calculate Height of Pentagonal Cupola?

Here are the different ways to Calculate Height of Pentagonal Cupola-

Height of Pentagonal Cupola=Edge Length of Pentagonal Cupola*sqrt(1-(1/4*cosec(pi/5)^(2)))
Height of Pentagonal Cupola=(Volume of Pentagonal Cupola/(1/6*(5+(4*sqrt(5)))))^(1/3)*sqrt(1-(1/4*cosec(pi/5)^(2)))
Height of Pentagonal Cupola=(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)*sqrt(1-(1/4*cosec(pi/5)^(2)))

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

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

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

Height of Pentagonal Cupola given Total Surface Area is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Height of Pentagonal Cupola given Total Surface Area can be measured.

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