Volume of Square Cupola given Height 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 [h]

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✖Volume of Square Cupola is the total quantity of three-dimensional space enclosed by the surface of the Square Cupola.ⓘ Volume of Square Cupola given Height [V]

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Formula

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Volume of Square Cupola given Height

Formula

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

Example

`"1884.817m³"=(1+(2*sqrt(2))/3)*("7m"/sqrt(1-(1/4*cosec(pi/4)^(2))))^3`

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Volume of Square Cupola given Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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.

STEP 1: Convert Input(s) to Base Unit

Height of Square Cupola: 7 Meter --> 7 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = (1+(2*sqrt(2))/3)*(h/sqrt(1-(1/4*cosec(pi/4)^(2))))^3 --> (1+(2*sqrt(2))/3)*(7/sqrt(1-(1/4*cosec(pi/4)^(2))))^3

Evaluating ... ...

V = 1884.81717045461

STEP 3: Convert Result to Output's Unit

1884.81717045461 Cubic Meter --> No Conversion Required

FINAL ANSWER

1884.81717045461 ≈ 1884.817 Cubic Meter <-- Volume of Square Cupola

(Calculation completed in 00.004 seconds)

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< 4 Volume of Square Cupola Calculators

Volume of Square Cupola given Surface to Volume Ratio

Go 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

Volume of Square Cupola given Height

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

Volume of Square Cupola given Total Surface Area

Go 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

Go Volume of Square Cupola = (1+(2*sqrt(2))/3)*Edge Length of Square Cupola^3

Volume of Square Cupola given Height Formula

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

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 Volume of Square Cupola given Height?

Volume of Square Cupola given Height calculator uses Volume of Square Cupola = (1+(2*sqrt(2))/3)*(Height of Square Cupola/sqrt(1-(1/4*cosec(pi/4)^(2))))^3 to calculate 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 calculate Volume of Square Cupola given Height using this online calculator? To use this online calculator for Volume of Square Cupola given Height, enter Height of Square Cupola (h) and hit the calculate button. Here is how the Volume of Square Cupola given Height calculation can be explained with given input values -> 1884.817 = (1+(2*sqrt(2))/3)*(7/sqrt(1-(1/4*cosec(pi/4)^(2))))^3.

FAQ

What is Volume of Square Cupola given Height?

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 and is represented as V = (1+(2*sqrt(2))/3)*(h/sqrt(1-(1/4*cosec(pi/4)^(2))))^3 or Volume of Square Cupola = (1+(2*sqrt(2))/3)*(Height of Square Cupola/sqrt(1-(1/4*cosec(pi/4)^(2))))^3. Height of Square Cupola is the vertical distance from the square face to the opposite octagonal face of the Square Cupola.

How to calculate Volume of Square Cupola given Height?

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 is calculated using Volume of Square Cupola = (1+(2*sqrt(2))/3)*(Height of Square Cupola/sqrt(1-(1/4*cosec(pi/4)^(2))))^3. To calculate Volume of Square Cupola given Height, you need Height of Square Cupola (h). With our tool, you need to enter the respective value for Height 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 Volume of Square Cupola?

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

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

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