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Height of Triangular Cupola given Total Surface Area Formula

GoHeight of Triangular Cupola Formula

GoHeight of Triangular Cupola given Volume Formula

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Height of Triangular Cupola is the vertical distance from the triangular face to the opposite hexagonal face of the Triangular Cupola. Check FAQs

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

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

Height of Triangular Cupola given Total Surface Area Example

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

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

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

8.1482 = \sqrt{\frac{730}{3 + \frac{5 \cdot \sqrt{3}}{2}}} \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{3})}^{2})}

8.1482m = \sqrt{\frac{730m²}{3 + \frac{5 \cdot \sqrt{3}}{2}}} \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{3})}^{2})}

8.1482 = \sqrt{\frac{730}{3 + \frac{5 \cdot \sqrt{3}}{2}}} \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{3})}^{2})}

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Height of Triangular Cupola given Total Surface Area Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

h = \sqrt{\frac{730m²}{3 + \frac{5 \cdot \sqrt{3}}{2}}} \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{π}{3})}^{2})}

Next Step Substitute values of Constants

∴

h = \sqrt{\frac{730m²}{3 + \frac{5 \cdot \sqrt{3}}{2}}} \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{3})}^{2})}

Next Step Prepare to Evaluate

∴

h = \sqrt{\frac{730}{3 + \frac{5 \cdot \sqrt{3}}{2}}} \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{3})}^{2})}

Next Step Evaluate

∴

h = 8.14816941871708m

LAST Step Rounding Answer

∴

h = 8.1482m

Height of Triangular Cupola given Total Surface Area Formula Elements

Variables

Constants

Functions

Height of Triangular Cupola

Height of Triangular Cupola is the vertical distance from the triangular face to the opposite hexagonal face of the Triangular Cupola.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Triangular Cupola

Total Surface Area of Triangular Cupola

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

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area of Triangular 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 Triangular Cupola

Go Height of Triangular Cupola

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

Go Height of Triangular Cupola given Volume

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

Go Height of Triangular Cupola given Surface to Volume Ratio

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

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

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

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

FAQs on Height of Triangular Cupola given Total Surface Area

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

The formula of Height of Triangular Cupola given Total Surface Area is expressed as Height of Triangular Cupola = sqrt(Total Surface Area of Triangular Cupola/(3+(5*sqrt(3))/2))*sqrt(1-(1/4*cosec(pi/3)^(2))). Here is an example- 8.148169 = sqrt(730/(3+(5*sqrt(3))/2))*sqrt(1-(1/4*cosec(pi/3)^(2))).

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

With Total Surface Area of Triangular Cupola (TSA) we can find Height of Triangular Cupola given Total Surface Area using the formula - Height of Triangular Cupola = sqrt(Total Surface Area of Triangular Cupola/(3+(5*sqrt(3))/2))*sqrt(1-(1/4*cosec(pi/3)^(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 Triangular Cupola?

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

Height of Triangular Cupola=Edge Length of Triangular Cupola*sqrt(1-(1/4*cosec(pi/3)^(2)))
Height of Triangular Cupola=((3*sqrt(2)*Volume of Triangular Cupola)/5)^(1/3)*sqrt(1-(1/4*cosec(pi/3)^(2)))
Height of Triangular Cupola=((3+(5*sqrt(3))/2)*(3*sqrt(2)))/(5*Surface to Volume Ratio of Triangular Cupola)*sqrt(1-(1/4*cosec(pi/3)^(2)))

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

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

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

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

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