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Height of Triangular Cupola given Surface to Volume Ratio Formula

GoHeight of Triangular Cupola Formula

GoHeight of Triangular Cupola given Total Surface Area 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 = \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})}

h - Height of Triangular Cupola?R_A/V - Surface to Volume Ratio of Triangular Cupola?π - Archimedes' constant?

Height of Triangular Cupola given Surface to Volume Ratio Example

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Here is how the Height of Triangular Cupola given Surface to Volume Ratio equation looks like with Units.

Here is how the Height of Triangular Cupola given Surface to Volume Ratio equation looks like.

8.4641 = \frac{(3 + \frac{5 \cdot \sqrt{3}}{2}) \cdot (3 \cdot \sqrt{2})}{5 \cdot 0.6} \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{3})}^{2})}

8.4641m = \frac{(3 + \frac{5 \cdot \sqrt{3}}{2}) \cdot (3 \cdot \sqrt{2})}{5 \cdot 0.6m⁻¹} \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{3})}^{2})}

8.4641 = \frac{(3 + \frac{5 \cdot \sqrt{3}}{2}) \cdot (3 \cdot \sqrt{2})}{5 \cdot 0.6} \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{3})}^{2})}

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Height of Triangular Cupola given Surface to Volume Ratio Solution

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

FIRST Step Consider the formula

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})}

Next Step Substitute values of Variables

∴

h = \frac{(3 + \frac{5 \cdot \sqrt{3}}{2}) \cdot (3 \cdot \sqrt{2})}{5 \cdot 0.6m⁻¹} \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{π}{3})}^{2})}

Next Step Substitute values of Constants

∴

h = \frac{(3 + \frac{5 \cdot \sqrt{3}}{2}) \cdot (3 \cdot \sqrt{2})}{5 \cdot 0.6m⁻¹} \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{3})}^{2})}

Next Step Prepare to Evaluate

∴

h = \frac{(3 + \frac{5 \cdot \sqrt{3}}{2}) \cdot (3 \cdot \sqrt{2})}{5 \cdot 0.6} \cdot \sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{3})}^{2})}

Next Step Evaluate

∴

h = 8.46410161513775m

LAST Step Rounding Answer

∴

h = 8.4641m

Height of Triangular Cupola given Surface to Volume Ratio 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

Surface to Volume Ratio of Triangular Cupola

Surface to Volume Ratio of Triangular Cupola is the numerical ratio of the total surface area of a Triangular Cupola to the volume of the Triangular Cupola.

Symbol: R_A/V

Measurement: Reciprocal LengthUnit: m⁻¹

Note: Value should be greater than 0.

Formulas to find Surface to Volume Ratio 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 Total Surface Area

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})}

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})}

How to Evaluate Height of Triangular Cupola given Surface to Volume Ratio?

Height of Triangular Cupola given Surface to Volume Ratio evaluator uses 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))) to evaluate the Height of Triangular Cupola, The Height of Triangular Cupola given Surface to Volume Ratio 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 surface to volume ratio of the Triangular Cupola. Height of Triangular Cupola is denoted by h symbol.

How to evaluate Height of Triangular Cupola given Surface to Volume Ratio using this online evaluator? To use this online evaluator for Height of Triangular Cupola given Surface to Volume Ratio, enter Surface to Volume Ratio of Triangular Cupola (R_A/V) and hit the calculate button.

FAQs on Height of Triangular Cupola given Surface to Volume Ratio

What is the formula to find Height of Triangular Cupola given Surface to Volume Ratio?

The formula of Height of Triangular Cupola given Surface to Volume Ratio is expressed as 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))). Here is an example- 8.464102 = ((3+(5*sqrt(3))/2)*(3*sqrt(2)))/(5*0.6)*sqrt(1-(1/4*cosec(pi/3)^(2))).

How to calculate Height of Triangular Cupola given Surface to Volume Ratio?

With Surface to Volume Ratio of Triangular Cupola (R_A/V) we can find Height of Triangular Cupola given Surface to Volume Ratio using the formula - 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))). This formula also uses Archimedes' constant and , Secant Function, cosecant , Square Root Function 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=sqrt(Total Surface Area of Triangular Cupola/(3+(5*sqrt(3))/2))*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)))

Can the Height of Triangular Cupola given Surface to Volume Ratio be negative?

No, the Height of Triangular Cupola given Surface to Volume Ratio, measured in Length cannot be negative.

Which unit is used to measure Height of Triangular Cupola given Surface to Volume Ratio?

Height of Triangular Cupola given Surface to Volume Ratio 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 Surface to Volume Ratio can be measured.

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