Volume of Pentagonal Cupola given Height Calculator

✖Height of Pentagonal Cupola is the vertical distance from the pentagonal face to the opposite decagonal face of the Pentagonal Cupola.ⓘ Height of Pentagonal Cupola [h]

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

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Volume of Pentagonal Cupola given Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Pentagonal Cupola = 1/6*(5+(4*sqrt(5)))*(Height of Pentagonal Cupola/sqrt(1-(1/4*cosec(pi/5)^(2))))^3
V = 1/6*(5+(4*sqrt(5)))*(h/sqrt(1-(1/4*cosec(pi/5)^(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 Pentagonal Cupola - (Measured in Cubic Meter) - Volume of Pentagonal Cupola is the total quantity of three-dimensional space enclosed by the surface of the Pentagonal Cupola.
Height of Pentagonal Cupola - (Measured in Meter) - Height of Pentagonal Cupola is the vertical distance from the pentagonal face to the opposite decagonal face of the Pentagonal Cupola.

STEP 1: Convert Input(s) to Base Unit

Height of Pentagonal Cupola: 5 Meter --> 5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V = 1/6*(5+(4*sqrt(5)))*(h/sqrt(1-(1/4*cosec(pi/5)^(2))))^3 --> 1/6*(5+(4*sqrt(5)))*(5/sqrt(1-(1/4*cosec(pi/5)^(2))))^3

Evaluating ... ...

V = 1999.23372406842

STEP 3: Convert Result to Output's Unit

1999.23372406842 Cubic Meter --> No Conversion Required

FINAL ANSWER

1999.23372406842 ≈ 1999.234 Cubic Meter <-- Volume of Pentagonal Cupola

(Calculation completed in 00.004 seconds)

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< Volume of Pentagonal Cupola Calculators

Volume of Pentagonal Cupola given Surface to Volume Ratio

LaTeX Go 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

Volume of Pentagonal Cupola given Total Surface Area

LaTeX Go 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 given Height

LaTeX Go Volume of Pentagonal Cupola = 1/6*(5+(4*sqrt(5)))*(Height of Pentagonal Cupola/sqrt(1-(1/4*cosec(pi/5)^(2))))^3

Volume of Pentagonal Cupola

LaTeX Go Volume of Pentagonal Cupola = 1/6*(5+(4*sqrt(5)))*Edge Length of Pentagonal Cupola^3

Volume of Pentagonal Cupola given Height Formula

LaTeX Go

Volume of Pentagonal Cupola = 1/6*(5+(4*sqrt(5)))*(Height of Pentagonal Cupola/sqrt(1-(1/4*cosec(pi/5)^(2))))^3
V = 1/6*(5+(4*sqrt(5)))*(h/sqrt(1-(1/4*cosec(pi/5)^(2))))^3

What is a Pentagonal 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 Pentagonal Cupola has 12 faces, 25 edges, and 15 vertices. Its top surface is a regular pentagon and the base surface is a regular decagon.

How to Calculate Volume of Pentagonal Cupola given Height?

Volume of Pentagonal Cupola given Height calculator 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 calculate 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 calculate Volume of Pentagonal Cupola given Height using this online calculator? To use this online calculator for Volume of Pentagonal Cupola given Height, enter Height of Pentagonal Cupola (h) and hit the calculate button. Here is how the Volume of Pentagonal Cupola given Height calculation can be explained with given input values -> 1999.234 = 1/6*(5+(4*sqrt(5)))*(5/sqrt(1-(1/4*cosec(pi/5)^(2))))^3.

FAQ

What is Volume of Pentagonal Cupola given Height?

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 and is represented as V = 1/6*(5+(4*sqrt(5)))*(h/sqrt(1-(1/4*cosec(pi/5)^(2))))^3 or Volume of Pentagonal Cupola = 1/6*(5+(4*sqrt(5)))*(Height of Pentagonal Cupola/sqrt(1-(1/4*cosec(pi/5)^(2))))^3. Height of Pentagonal Cupola is the vertical distance from the pentagonal face to the opposite decagonal face of the Pentagonal Cupola.

How to calculate Volume of Pentagonal Cupola given Height?

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 is calculated using Volume of Pentagonal Cupola = 1/6*(5+(4*sqrt(5)))*(Height of Pentagonal Cupola/sqrt(1-(1/4*cosec(pi/5)^(2))))^3. To calculate Volume of Pentagonal Cupola given Height, you need Height of Pentagonal Cupola (h). With our tool, you need to enter the respective value for Height of Pentagonal 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 Pentagonal Cupola?

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

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

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