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Height of Square Cupola Formula

GoHeight of Square Cupola given Total Surface Area Formula

GoHeight of Square Cupola given Volume Formula

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

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

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

Height of Square Cupola Example

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

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

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

7.0711 = 10 \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{4})}^{2})}

7.0711m = 10m \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{4})}^{2})}

7.0711 = 10 \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{4})}^{2})}

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Height of Square Cupola Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

h = 10m \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{π}{4})}^{2})}

Next Step Substitute values of Constants

∴

h = 10m \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{4})}^{2})}

Next Step Prepare to Evaluate

∴

h = 10 \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{4})}^{2})}

Next Step Evaluate

∴

h = 7.07106781186547m

LAST Step Rounding Answer

∴

h = 7.0711m

Height of Square Cupola Formula Elements

Variables

Constants

Functions

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

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

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 Square Cupola

Go Height of Square Cupola given Total Surface Area

h = \sqrt{\frac{TSA}{7 + (2 \cdot \sqrt{2}) + \sqrt{3}}} \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{π}{4})}^{2})}

Go Height of Square Cupola given Volume

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

Go Height of Square Cupola given Surface to Volume Ratio

h = \frac{(7 + (2 \cdot \sqrt{2}) + \sqrt{3}) \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{π}{4})}^{2})}}{(1 + \frac{2 \cdot \sqrt{2}}{3}) \cdot R A/V}

How to Evaluate Height of Square Cupola?

Height of Square Cupola evaluator uses Height of Square Cupola = Edge Length of Square Cupola*sqrt(1-(1/4*cosec(pi/4)^(2))) to evaluate the Height of Square Cupola, The Height of Square Cupola formula is defined as the vertical distance from the square face to the opposite octagonal face of the Square Cupola. Height of Square Cupola is denoted by h symbol.

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

FAQs on Height of Square Cupola

What is the formula to find Height of Square Cupola?

The formula of Height of Square Cupola is expressed as Height of Square Cupola = Edge Length of Square Cupola*sqrt(1-(1/4*cosec(pi/4)^(2))). Here is an example- 7.071068 = 10*sqrt(1-(1/4*cosec(pi/4)^(2))).

How to calculate Height of Square Cupola?

With Edge Length of Square Cupola (l_e) we can find Height of Square Cupola using the formula - Height of Square Cupola = Edge Length 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 Height of Square Cupola?

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

Height of Square Cupola=sqrt(Total Surface Area of Square Cupola/(7+(2*sqrt(2))+sqrt(3)))*sqrt(1-(1/4*cosec(pi/4)^(2)))
Height of Square Cupola=(Volume of Square Cupola/(1+(2*sqrt(2))/3))^(1/3)*sqrt(1-(1/4*cosec(pi/4)^(2)))
Height of Square Cupola=((7+(2*sqrt(2))+sqrt(3))*sqrt(1-(1/4*cosec(pi/4)^(2))))/((1+(2*sqrt(2))/3)*Surface to Volume Ratio of Square Cupola)

Can the Height of Square Cupola be negative?

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

Which unit is used to measure Height of Square Cupola?

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

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