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Volume of Square Cupola given Height Formula

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GoVolume of Square Cupola given Total Surface Area Formula

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

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

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

Volume of Square Cupola given Height Example

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

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

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

1884.8172 = (1 + \frac{2 \cdot \sqrt{2}}{3}) \cdot {(\frac{7}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{4})}^{2})}})}^{3}

1884.8172m³ = (1 + \frac{2 \cdot \sqrt{2}}{3}) \cdot {(\frac{7m}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{4})}^{2})}})}^{3}

1884.8172 = (1 + \frac{2 \cdot \sqrt{2}}{3}) \cdot {(\frac{7}{\sqrt{1 - (\frac{1}{4} \cdot \cos e c {(\frac{3.1416}{4})}^{2})}})}^{3}

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Volume of Square Cupola given Height Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Substitute values of Constants

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

V = 1884.81717045461m³

LAST Step Rounding Answer

∴

V = 1884.8172m³

Volume of Square Cupola given Height Formula Elements

Variables

Constants

Functions

Volume of Square Cupola

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

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Square Cupola

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

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 Square Cupola

Go Volume of Square Cupola

V = (1 + \frac{2 \cdot \sqrt{2}}{3}) \cdot {l e}^{3}

Go Volume of Square Cupola given Total Surface Area

V = (1 + \frac{2 \cdot \sqrt{2}}{3}) \cdot {(\frac{TSA}{7 + (2 \cdot \sqrt{2}) + \sqrt{3}})}^{\frac{3}{2}}

Go Volume of Square Cupola given Surface to Volume Ratio

V = (1 + \frac{2 \cdot \sqrt{2}}{3}) \cdot {(\frac{7 + (2 \cdot \sqrt{2}) + \sqrt{3}}{(1 + \frac{2 \cdot \sqrt{2}}{3}) \cdot R A/V})}^{3}

How to Evaluate Volume of Square Cupola given Height?

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

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

FAQs on Volume of Square Cupola given Height

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

The formula of Volume of Square Cupola given Height is expressed as Volume of Square Cupola = (1+(2*sqrt(2))/3)*(Height of Square Cupola/sqrt(1-(1/4*cosec(pi/4)^(2))))^3. Here is an example- 1884.817 = (1+(2*sqrt(2))/3)*(7/sqrt(1-(1/4*cosec(pi/4)^(2))))^3.

How to calculate Volume of Square Cupola given Height?

With Height of Square Cupola (h) we can find Volume of Square Cupola given Height using the formula - Volume of Square Cupola = (1+(2*sqrt(2))/3)*(Height of Square Cupola/sqrt(1-(1/4*cosec(pi/4)^(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 Square Cupola?

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

Volume of Square Cupola=(1+(2*sqrt(2))/3)*Edge Length of Square Cupola^3
Volume of Square Cupola=(1+(2*sqrt(2))/3)*(Total Surface Area of Square Cupola/(7+(2*sqrt(2))+sqrt(3)))^(3/2)
Volume of Square Cupola=(1+(2*sqrt(2))/3)*((7+(2*sqrt(2))+sqrt(3))/((1+(2*sqrt(2))/3)*Surface to Volume Ratio of Square Cupola))^3

Can the Volume of Square Cupola given Height be negative?

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

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

Volume of Square 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 Square Cupola given Height can be measured.

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