Height of Square Cupola given Volume Calculator

✖Height of Square Cupola is the vertical distance from the square face to the opposite octagonal face of the Square Cupola.ⓘ Height of Square Cupola given Volume [h]

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Formula

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Height of Square Cupola given Volume

Formula

`"h" = ("V"/(1+(2*sqrt(2))/3))^(1/3)*sqrt(1-(1/4*cosec(pi/4)^(2)))`

Example

`"7.018746m"=("1900m³"/(1+(2*sqrt(2))/3))^(1/3)*sqrt(1-(1/4*cosec(pi/4)^(2)))`

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Height of Square Cupola given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of Square Cupola = (Volume of Square Cupola/(1+(2*sqrt(2))/3))^(1/3)*sqrt(1-(1/4*cosec(pi/4)^(2)))
h = (V/(1+(2*sqrt(2))/3))^(1/3)*sqrt(1-(1/4*cosec(pi/4)^(2)))
This formula uses 1 Constants, 3 Functions, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

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., sec(Angle)
cosec - The cosecant function is a trigonometric function that is the reciprocal of the sine function., 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., sqrt(Number)

Variables Used

Height of Square Cupola - (Measured in Meter) - Height of Square Cupola is the vertical distance from the square face to the opposite octagonal face of the Square Cupola.
Volume of Square Cupola - (Measured in Cubic Meter) - Volume of Square Cupola is the total quantity of three-dimensional space enclosed by the surface of the Square Cupola.

STEP 1: Convert Input(s) to Base Unit

Volume of Square Cupola: 1900 Cubic Meter --> 1900 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = (V/(1+(2*sqrt(2))/3))^(1/3)*sqrt(1-(1/4*cosec(pi/4)^(2))) --> (1900/(1+(2*sqrt(2))/3))^(1/3)*sqrt(1-(1/4*cosec(pi/4)^(2)))

Evaluating ... ...

h = 7.01874553240278

STEP 3: Convert Result to Output's Unit

7.01874553240278 Meter --> No Conversion Required

FINAL ANSWER

7.01874553240278 ≈ 7.018746 Meter <-- Height of Square Cupola

(Calculation completed in 00.004 seconds)

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< 4 Height of Square Cupola Calculators

Height of Square Cupola given Surface to Volume Ratio

Go Height of Square Cupola = ((7+(2*sqrt(2))+sqrt(3))*sqrt(1-(1/4*cosec(pi/4)^(2))))/((1+(2*sqrt(2))/3)*Surface to Volume Ratio of Square Cupola)

Height of Square Cupola given Total Surface Area

Go Height of Square Cupola = sqrt(Total Surface Area of Square Cupola/(7+(2*sqrt(2))+sqrt(3)))*sqrt(1-(1/4*cosec(pi/4)^(2)))

Height of Square Cupola given Volume

Go Height of Square Cupola = (Volume of Square Cupola/(1+(2*sqrt(2))/3))^(1/3)*sqrt(1-(1/4*cosec(pi/4)^(2)))

Height of Square Cupola

Go Height of Square Cupola = Edge Length of Square Cupola*sqrt(1-(1/4*cosec(pi/4)^(2)))

Height of Square Cupola given Volume Formula

Height of Square Cupola = (Volume of Square Cupola/(1+(2*sqrt(2))/3))^(1/3)*sqrt(1-(1/4*cosec(pi/4)^(2)))
h = (V/(1+(2*sqrt(2))/3))^(1/3)*sqrt(1-(1/4*cosec(pi/4)^(2)))

What is a Square Cupola?

A cupola is a polyhedron with two opposite polygons, of which one has twice as many vertices as the other and with alternating triangles and quadrangles as side faces. When all faces of the cupola are regular, then the cupola itself is regular and is a Johnson solid. There are three regular cupolae, the triangular, the square, and the pentagonal cupola. A Square Cupola has 10 faces, 20 edges, and 12 vertices. Its top surface is a square and the base surface is a regular octagon.

How to Calculate Height of Square Cupola given Volume?

Height of Square Cupola given Volume calculator uses Height of Square Cupola = (Volume of Square Cupola/(1+(2*sqrt(2))/3))^(1/3)*sqrt(1-(1/4*cosec(pi/4)^(2))) to calculate the Height of Square Cupola, The Height of Square Cupola given Volume formula is defined as the vertical distance from the square face to the opposite octagonal face of the Square Cupola and is calculated using the volume of the Square Cupola. Height of Square Cupola is denoted by h symbol.

How to calculate Height of Square Cupola given Volume using this online calculator? To use this online calculator for Height of Square Cupola given Volume, enter Volume of Square Cupola (V) and hit the calculate button. Here is how the Height of Square Cupola given Volume calculation can be explained with given input values -> 7.018746 = (1900/(1+(2*sqrt(2))/3))^(1/3)*sqrt(1-(1/4*cosec(pi/4)^(2))).

FAQ

What is Height of Square Cupola given Volume?

The Height of Square Cupola given Volume formula is defined as the vertical distance from the square face to the opposite octagonal face of the Square Cupola and is calculated using the volume of the Square Cupola and is represented as h = (V/(1+(2*sqrt(2))/3))^(1/3)*sqrt(1-(1/4*cosec(pi/4)^(2))) or Height of Square Cupola = (Volume of Square Cupola/(1+(2*sqrt(2))/3))^(1/3)*sqrt(1-(1/4*cosec(pi/4)^(2))). Volume of Square Cupola is the total quantity of three-dimensional space enclosed by the surface of the Square Cupola.

How to calculate Height of Square Cupola given Volume?

The Height of Square Cupola given Volume formula is defined as the vertical distance from the square face to the opposite octagonal face of the Square Cupola and is calculated using the volume of the Square Cupola is calculated using Height of Square Cupola = (Volume of Square Cupola/(1+(2*sqrt(2))/3))^(1/3)*sqrt(1-(1/4*cosec(pi/4)^(2))). To calculate Height of Square Cupola given Volume, you need Volume of Square Cupola (V). With our tool, you need to enter the respective value for Volume of Square Cupola and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Height of Square Cupola?

In this formula, Height of Square Cupola uses Volume of Square Cupola. We can use 3 other way(s) to calculate the same, which is/are as follows -

Height of Square Cupola = Edge Length of Square Cupola*sqrt(1-(1/4*cosec(pi/4)^(2)))
Height of Square Cupola = sqrt(Total Surface Area of Square Cupola/(7+(2*sqrt(2))+sqrt(3)))*sqrt(1-(1/4*cosec(pi/4)^(2)))
Height of Square Cupola = ((7+(2*sqrt(2))+sqrt(3))*sqrt(1-(1/4*cosec(pi/4)^(2))))/((1+(2*sqrt(2))/3)*Surface to Volume Ratio of Square Cupola)

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