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Height of Square Cupola given Total Surface Area Formula

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

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

Height of Square Cupola given Total Surface Area Example

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

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

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

7.0831 = \sqrt{\frac{1160}{7 + (2 \cdot \sqrt{2}) + \sqrt{3}}} \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{4})}^{2})}

7.0831m = \sqrt{\frac{1160m²}{7 + (2 \cdot \sqrt{2}) + \sqrt{3}}} \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{4})}^{2})}

7.0831 = \sqrt{\frac{1160}{7 + (2 \cdot \sqrt{2}) + \sqrt{3}}} \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{4})}^{2})}

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Height of Square Cupola given Total Surface Area Solution

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

FIRST Step Consider the formula

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})}

Next Step Substitute values of Variables

∴

h = \sqrt{\frac{1160m²}{7 + (2 \cdot \sqrt{2}) + \sqrt{3}}} \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{π}{4})}^{2})}

Next Step Substitute values of Constants

∴

h = \sqrt{\frac{1160m²}{7 + (2 \cdot \sqrt{2}) + \sqrt{3}}} \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{4})}^{2})}

Next Step Prepare to Evaluate

∴

h = \sqrt{\frac{1160}{7 + (2 \cdot \sqrt{2}) + \sqrt{3}}} \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{4})}^{2})}

Next Step Evaluate

∴

h = 7.08314450877644m

LAST Step Rounding Answer

∴

h = 7.0831m

Height of Square Cupola given Total Surface Area 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

Total Surface Area of Square Cupola

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

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area 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

h = l e \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 given Total Surface Area?

Height of Square Cupola given Total Surface Area evaluator uses 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))) to evaluate the Height of Square Cupola, The Height of Square Cupola given Total Surface Area formula is defined as the vertical distance from the square face to the opposite octagonal face of the Square Cupola and is calculated using the total surface area of the Square Cupola. Height of Square Cupola is denoted by h symbol.

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

FAQs on Height of Square Cupola given Total Surface Area

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

The formula of Height of Square Cupola given Total Surface Area is expressed as 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))). Here is an example- 7.083145 = sqrt(1160/(7+(2*sqrt(2))+sqrt(3)))*sqrt(1-(1/4*cosec(pi/4)^(2))).

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

With Total Surface Area of Square Cupola (TSA) we can find Height of Square Cupola given Total Surface Area using the formula - 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))). 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=Edge Length of Square Cupola*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 given Total Surface Area be negative?

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

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

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

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