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Volume of Pentagonal Cupola given Height Formula

GoVolume of Pentagonal Cupola Formula

GoVolume of Pentagonal Cupola given Total Surface Area Formula

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

V = \frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5})) \cdot {(\frac{h}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{π}{5})}^{2})}})}^{3}

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

Volume of Pentagonal Cupola given Height Example

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

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

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

1999.2337 = \frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5})) \cdot {(\frac{5}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{5})}^{2})}})}^{3}

1999.2337m³ = \frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5})) \cdot {(\frac{5m}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{5})}^{2})}})}^{3}

1999.2337 = \frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5})) \cdot {(\frac{5}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{5})}^{2})}})}^{3}

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Volume of Pentagonal Cupola given Height Solution

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

FIRST Step Consider the formula

V = \frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5})) \cdot {(\frac{h}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{π}{5})}^{2})}})}^{3}

Next Step Substitute values of Variables

∴

V = \frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5})) \cdot {(\frac{5m}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{π}{5})}^{2})}})}^{3}

Next Step Substitute values of Constants

∴

V = \frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5})) \cdot {(\frac{5m}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{5})}^{2})}})}^{3}

Next Step Prepare to Evaluate

∴

V = \frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5})) \cdot {(\frac{5}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{5})}^{2})}})}^{3}

Next Step Evaluate

∴

V = 1999.23372406842m³

LAST Step Rounding Answer

∴

V = 1999.2337m³

Volume of Pentagonal Cupola given Height Formula Elements

Variables

Constants

Functions

Volume of Pentagonal Cupola

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

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Pentagonal Cupola

Height of Pentagonal Cupola

Height of Pentagonal Cupola is the vertical distance from the pentagonal face to the opposite decagonal face of the Pentagonal Cupola.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Pentagonal 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 Pentagonal Cupola

Go Volume of Pentagonal Cupola

V = \frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5})) \cdot {l e}^{3}

Go Volume of Pentagonal Cupola given Total Surface Area

V = \frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5})) \cdot {(\frac{TSA}{\frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))})})}^{\frac{3}{2}}

Go Volume of Pentagonal Cupola given Surface to Volume Ratio

V = \frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5})) \cdot {(\frac{\frac{1}{4} \cdot (20 + (5 \cdot \sqrt{3}) + \sqrt{5 \cdot (145 + (62 \cdot \sqrt{5}))})}{\frac{1}{6} \cdot (5 + (4 \cdot \sqrt{5})) \cdot R A/V})}^{3}

How to Evaluate Volume of Pentagonal Cupola given Height?

Volume of Pentagonal Cupola given Height evaluator uses Volume of Pentagonal Cupola = 1/6*(5+(4*sqrt(5)))*(Height of Pentagonal Cupola/sqrt(1-(1/4*cosec(pi/5)^(2))))^3 to evaluate the Volume of Pentagonal Cupola, The Volume of Pentagonal Cupola given Height formula is defined as the total quantity of three-dimensional space enclosed by the surface of the Pentagonal Cupola and is calculated using the height of the Pentagonal Cupola. Volume of Pentagonal Cupola is denoted by V symbol.

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

FAQs on Volume of Pentagonal Cupola given Height

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

The formula of Volume of Pentagonal Cupola given Height is expressed as Volume of Pentagonal Cupola = 1/6*(5+(4*sqrt(5)))*(Height of Pentagonal Cupola/sqrt(1-(1/4*cosec(pi/5)^(2))))^3. Here is an example- 1999.234 = 1/6*(5+(4*sqrt(5)))*(5/sqrt(1-(1/4*cosec(pi/5)^(2))))^3.

How to calculate Volume of Pentagonal Cupola given Height?

With Height of Pentagonal Cupola (h) we can find Volume of Pentagonal Cupola given Height using the formula - Volume of Pentagonal Cupola = 1/6*(5+(4*sqrt(5)))*(Height of Pentagonal Cupola/sqrt(1-(1/4*cosec(pi/5)^(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 Pentagonal Cupola?

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

Volume of Pentagonal Cupola=1/6*(5+(4*sqrt(5)))*Edge Length of Pentagonal Cupola^3
Volume of Pentagonal Cupola=1/6*(5+(4*sqrt(5)))*(Total Surface Area of Pentagonal Cupola/(1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5)))))))^(3/2)
Volume of Pentagonal Cupola=1/6*(5+(4*sqrt(5)))*((1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5))))))/(1/6*(5+(4*sqrt(5)))*Surface to Volume Ratio of Pentagonal Cupola))^3

Can the Volume of Pentagonal Cupola given Height be negative?

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

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

Volume of Pentagonal 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 Pentagonal Cupola given Height can be measured.

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