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Edge Length of Pentagonal Cupola given Height Formula

GoEdge Length of Pentagonal Cupola given Total Surface Area Formula

GoEdge Length of Pentagonal Cupola given Volume Formula

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Edge Length of Pentagonal Cupola is the length of any edge of the Pentagonal Cupola. Check FAQs

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

l_e - Edge Length of Pentagonal Cupola?h - Height of Pentagonal Cupola?π - Archimedes' constant?

Edge Length of Pentagonal Cupola given Height Example

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Here is how the Edge Length of Pentagonal Cupola given Height equation looks like with Values.

Here is how the Edge Length of Pentagonal Cupola given Height equation looks like with Units.

Here is how the Edge Length of Pentagonal Cupola given Height equation looks like.

9.5106 = \frac{5}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{5})}^{2})}}

9.5106m = \frac{5m}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{5})}^{2})}}

9.5106 = \frac{5}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{5})}^{2})}}

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Edge Length of Pentagonal Cupola given Height Solution

Follow our step by step solution on how to calculate Edge Length of Pentagonal Cupola given Height?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Substitute values of Constants

∴

l e = \frac{5m}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{5})}^{2})}}

Next Step Prepare to Evaluate

∴

l e = \frac{5}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{5})}^{2})}}

Next Step Evaluate

∴

l e = 9.51056516295153m

LAST Step Rounding Answer

∴

l e = 9.5106m

Edge Length of Pentagonal Cupola given Height Formula Elements

Variables

Constants

Functions

Edge Length of Pentagonal Cupola

Edge Length of Pentagonal Cupola is the length of any edge of the Pentagonal Cupola.

Symbol: l_e

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length 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 Edge Length of Pentagonal Cupola

Go Edge Length of Pentagonal Cupola given Total Surface Area

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

Go Edge Length of Pentagonal Cupola given Volume

l e = {(\frac{V}{\frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5}))})}^{\frac{1}{3}}

Go Edge Length of Pentagonal Cupola given Surface to Volume Ratio

l e = \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}

How to Evaluate Edge Length of Pentagonal Cupola given Height?

Edge Length of Pentagonal Cupola given Height evaluator uses Edge Length of Pentagonal Cupola = Height of Pentagonal Cupola/sqrt(1-(1/4*cosec(pi/5)^2)) to evaluate the Edge Length of Pentagonal Cupola, The Edge Length of Pentagonal Cupola given Height formula is defined as the length of any edge of the Pentagonal Cupola and is calculated using the height of the Pentagonal Cupola. Edge Length of Pentagonal Cupola is denoted by l_e symbol.

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

FAQs on Edge Length of Pentagonal Cupola given Height

What is the formula to find Edge Length of Pentagonal Cupola given Height?

The formula of Edge Length of Pentagonal Cupola given Height is expressed as Edge Length of Pentagonal Cupola = Height of Pentagonal Cupola/sqrt(1-(1/4*cosec(pi/5)^2)). Here is an example- 9.510565 = 5/sqrt(1-(1/4*cosec(pi/5)^2)).

How to calculate Edge Length of Pentagonal Cupola given Height?

With Height of Pentagonal Cupola (h) we can find Edge Length of Pentagonal Cupola given Height using the formula - Edge Length of Pentagonal Cupola = Height of Pentagonal Cupola/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 Edge Length of Pentagonal Cupola?

Here are the different ways to Calculate Edge Length of Pentagonal Cupola-

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

Can the Edge Length of Pentagonal Cupola given Height be negative?

No, the Edge Length of Pentagonal Cupola given Height, measured in Length cannot be negative.

Which unit is used to measure Edge Length of Pentagonal Cupola given Height?

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

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