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Edge Length of Square Cupola given Height Formula

GoEdge Length of Square Cupola given Total Surface Area Formula

GoEdge Length of Square Cupola given Volume Formula

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

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

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

Edge Length of Square Cupola given Height Example

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

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

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

9.8995 = \frac{7}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{4})}^{2})}}

9.8995m = \frac{7m}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{4})}^{2})}}

9.8995 = \frac{7}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{4})}^{2})}}

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Edge Length of Square Cupola given Height Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

l e = \frac{7m}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{π}{4})}^{2})}}

Next Step Substitute values of Constants

∴

l e = \frac{7m}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{4})}^{2})}}

Next Step Prepare to Evaluate

∴

l e = \frac{7}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{4})}^{2})}}

Next Step Evaluate

∴

l e = 9.89949493661167m

LAST Step Rounding Answer

∴

l e = 9.8995m

Edge Length of Square Cupola given Height Formula Elements

Variables

Constants

Functions

Edge Length of Square Cupola

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

Symbol: l_e

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length of Square Cupola

Height of Square Cupola

Height of Square Cupola is the vertical distance from the square face to the opposite octagonal face of the Square Cupola.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Square 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 Square Cupola

Go Edge Length of Square Cupola given Total Surface Area

l e = \sqrt{\frac{TSA}{7 + (2 \cdot \sqrt{2}) + \sqrt{3}}}

Go Edge Length of Square Cupola given Volume

l e = {(\frac{V}{1 + \frac{2 \cdot \sqrt{2}}{3}})}^{\frac{1}{3}}

Go Edge Length of Square Cupola given Surface to Volume Ratio

l e = \frac{7 + (2 \cdot \sqrt{2}) + \sqrt{3}}{(1 + \frac{2 \cdot \sqrt{2}}{3}) \cdot R A/V}

How to Evaluate Edge Length of Square Cupola given Height?

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

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

FAQs on Edge Length of Square Cupola given Height

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

The formula of Edge Length of Square Cupola given Height is expressed as Edge Length of Square Cupola = Height of Square Cupola/sqrt(1-(1/4*cosec(pi/4)^(2))). Here is an example- 9.899495 = 7/sqrt(1-(1/4*cosec(pi/4)^(2))).

How to calculate Edge Length of Square Cupola given Height?

With Height of Square Cupola (h) we can find Edge Length of Square Cupola given Height using the formula - Edge Length of Square Cupola = Height of Square Cupola/sqrt(1-(1/4*cosec(pi/4)^(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 Square Cupola?

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

Edge Length of Square Cupola=sqrt(Total Surface Area of Square Cupola/(7+(2*sqrt(2))+sqrt(3)))
Edge Length of Square Cupola=(Volume of Square Cupola/(1+(2*sqrt(2))/3))^(1/3)
Edge Length of Square Cupola=(7+(2*sqrt(2))+sqrt(3))/((1+(2*sqrt(2))/3)*Surface to Volume Ratio of Square Cupola)

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

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

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

Edge Length of Square 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 Square Cupola given Height can be measured.

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