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Volume of Triangular Cupola given Height Formula

GoVolume of Triangular Cupola Formula

GoVolume of Triangular Cupola given Total Surface Area Formula

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Volume of Triangular Cupola is the total quantity of three-dimensional space enclosed by the surface of the Triangular Cupola. Check FAQs

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

V - Volume of Triangular Cupola?h - Height of Triangular Cupola?π - Archimedes' constant?

Volume of Triangular Cupola given Height Example

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Here is how the Volume of Triangular Cupola given Height equation looks like with Values.

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

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

1108.5125 = \frac{5}{3 \cdot \sqrt{2}} \cdot {(\frac{8}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{3})}^{2})}})}^{3}

1108.5125m³ = \frac{5}{3 \cdot \sqrt{2}} \cdot {(\frac{8m}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{3})}^{2})}})}^{3}

1108.5125 = \frac{5}{3 \cdot \sqrt{2}} \cdot {(\frac{8}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{3})}^{2})}})}^{3}

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Volume of Triangular Cupola given Height Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

V = \frac{5}{3 \cdot \sqrt{2}} \cdot {(\frac{8m}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{π}{3})}^{2})}})}^{3}

Next Step Substitute values of Constants

∴

V = \frac{5}{3 \cdot \sqrt{2}} \cdot {(\frac{8m}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{3})}^{2})}})}^{3}

Next Step Prepare to Evaluate

∴

V = \frac{5}{3 \cdot \sqrt{2}} \cdot {(\frac{8}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{3})}^{2})}})}^{3}

Next Step Evaluate

∴

V = 1108.51251684408m³

LAST Step Rounding Answer

∴

V = 1108.5125m³

Volume of Triangular Cupola given Height Formula Elements

Variables

Constants

Functions

Volume of Triangular Cupola

Volume of Triangular Cupola is the total quantity of three-dimensional space enclosed by the surface of the Triangular Cupola.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Triangular Cupola

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

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 Volume of Triangular Cupola

Go Volume of Triangular Cupola

V = \frac{5}{3 \cdot \sqrt{2}} \cdot {l e}^{3}

Go Volume of Triangular Cupola given Total Surface Area

V = \frac{5}{3 \cdot \sqrt{2}} \cdot {(\frac{TSA}{3 + \frac{5 \cdot \sqrt{3}}{2}})}^{\frac{3}{2}}

Go Volume of Triangular Cupola given Surface to Volume Ratio

V = \frac{5}{3 \cdot \sqrt{2}} \cdot {(\frac{(3 + \frac{5 \cdot \sqrt{3}}{2}) \cdot (3 \cdot \sqrt{2})}{5 \cdot R A/V})}^{3}

How to Evaluate Volume of Triangular Cupola given Height?

Volume of Triangular Cupola given Height evaluator uses Volume of Triangular Cupola = 5/(3*sqrt(2))*(Height of Triangular Cupola/sqrt(1-(1/4*cosec(pi/3)^(2))))^3 to evaluate the Volume of Triangular Cupola, The Volume of Triangular Cupola given Height formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Triangular Cupola and is calculated using the height of the Triangular Cupola. Volume of Triangular Cupola is denoted by V symbol.

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

FAQs on Volume of Triangular Cupola given Height

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

The formula of Volume of Triangular Cupola given Height is expressed as Volume of Triangular Cupola = 5/(3*sqrt(2))*(Height of Triangular Cupola/sqrt(1-(1/4*cosec(pi/3)^(2))))^3. Here is an example- 1108.513 = 5/(3*sqrt(2))*(8/sqrt(1-(1/4*cosec(pi/3)^(2))))^3.

How to calculate Volume of Triangular Cupola given Height?

With Height of Triangular Cupola (h) we can find Volume of Triangular Cupola given Height using the formula - Volume of Triangular Cupola = 5/(3*sqrt(2))*(Height of Triangular Cupola/sqrt(1-(1/4*cosec(pi/3)^(2))))^3. This formula also uses Archimedes' constant and , Secant (sec), Cosecant (cosec), Square Root (sqrt) function(s).

What are the other ways to Calculate Volume of Triangular Cupola?

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

Volume of Triangular Cupola=5/(3*sqrt(2))*Edge Length of Triangular Cupola^(3)
Volume of Triangular Cupola=5/(3*sqrt(2))*(Total Surface Area of Triangular Cupola/(3+(5*sqrt(3))/2))^(3/2)
Volume of Triangular Cupola=5/(3*sqrt(2))*(((3+(5*sqrt(3))/2)*(3*sqrt(2)))/(5*Surface to Volume Ratio of Triangular Cupola))^(3)

Can the Volume of Triangular Cupola given Height be negative?

No, the Volume of Triangular Cupola given Height, measured in Volume cannot be negative.

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

Volume of Triangular Cupola given Height is usually measured using the Cubic Meter[m³] for Volume. Cubic Centimeter[m³], Cubic Millimeter[m³], Liter[m³] are the few other units in which Volume of Triangular Cupola given Height can be measured.

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