Height of Pentagonal Cupola given Volume Calculator

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

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✖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 given Volume [h]

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Height of Pentagonal Cupola given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

STEP 1: Convert Input(s) to Base Unit

Volume of Pentagonal Cupola: 2300 Cubic Meter --> 2300 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = (V/(1/6*(5+(4*sqrt(5)))))^(1/3)*sqrt(1-(1/4*cosec(pi/5)^(2))) --> (2300/(1/6*(5+(4*sqrt(5)))))^(1/3)*sqrt(1-(1/4*cosec(pi/5)^(2)))

Evaluating ... ...

h = 5.23911695286645

STEP 3: Convert Result to Output's Unit

5.23911695286645 Meter --> No Conversion Required

FINAL ANSWER

5.23911695286645 ≈ 5.239117 Meter <-- Height of Pentagonal Cupola

(Calculation completed in 00.004 seconds)

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< Height of Pentagonal Cupola Calculators

Height of Pentagonal Cupola given Surface to Volume Ratio

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

Height of Pentagonal Cupola given Total Surface Area

LaTeX Go Height of Pentagonal Cupola = sqrt(Total Surface Area of Pentagonal Cupola/(1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5)))))))*sqrt(1-(1/4*cosec(pi/5)^(2)))

Height of Pentagonal Cupola given Volume

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

Height of Pentagonal Cupola

LaTeX Go Height of Pentagonal Cupola = Edge Length of Pentagonal Cupola*sqrt(1-(1/4*cosec(pi/5)^(2)))

Height of Pentagonal Cupola given Volume Formula

LaTeX Go

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

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 Height of Pentagonal Cupola given Volume?

Height of Pentagonal Cupola given Volume calculator uses Height of Pentagonal Cupola = (Volume of Pentagonal Cupola/(1/6*(5+(4*sqrt(5)))))^(1/3)*sqrt(1-(1/4*cosec(pi/5)^(2))) to calculate the Height of Pentagonal Cupola, The Height of Pentagonal Cupola given Volume formula is defined as the vertical distance from the pentagonal face to the opposite decagonal face of the Pentagonal Cupola and is calculated using the volume of the Pentagonal Cupola. Height of Pentagonal Cupola is denoted by h symbol.

How to calculate Height of Pentagonal Cupola given Volume using this online calculator? To use this online calculator for Height of Pentagonal Cupola given Volume, enter Volume of Pentagonal Cupola (V) and hit the calculate button. Here is how the Height of Pentagonal Cupola given Volume calculation can be explained with given input values -> 5.239117 = (2300/(1/6*(5+(4*sqrt(5)))))^(1/3)*sqrt(1-(1/4*cosec(pi/5)^(2))).

FAQ

What is Height of Pentagonal Cupola given Volume?

The Height of Pentagonal Cupola given Volume formula is defined as the vertical distance from the pentagonal face to the opposite decagonal face of the Pentagonal Cupola and is calculated using the volume of the Pentagonal Cupola and is represented as h = (V/(1/6*(5+(4*sqrt(5)))))^(1/3)*sqrt(1-(1/4*cosec(pi/5)^(2))) or Height of Pentagonal Cupola = (Volume of Pentagonal Cupola/(1/6*(5+(4*sqrt(5)))))^(1/3)*sqrt(1-(1/4*cosec(pi/5)^(2))). Volume of Pentagonal Cupola is the total quantity of three-dimensional space enclosed by the surface of the Pentagonal Cupola.

How to calculate Height of Pentagonal Cupola given Volume?

The Height of Pentagonal Cupola given Volume formula is defined as the vertical distance from the pentagonal face to the opposite decagonal face of the Pentagonal Cupola and is calculated using the volume of the Pentagonal Cupola is calculated using Height of Pentagonal Cupola = (Volume of Pentagonal Cupola/(1/6*(5+(4*sqrt(5)))))^(1/3)*sqrt(1-(1/4*cosec(pi/5)^(2))). To calculate Height of Pentagonal Cupola given Volume, you need Volume of Pentagonal Cupola (V). With our tool, you need to enter the respective value for Volume 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 Height of Pentagonal Cupola?

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

Height of Pentagonal Cupola = Edge Length of Pentagonal Cupola*sqrt(1-(1/4*cosec(pi/5)^(2)))
Height of Pentagonal Cupola = sqrt(Total Surface Area of Pentagonal Cupola/(1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5)))))))*sqrt(1-(1/4*cosec(pi/5)^(2)))
Height of Pentagonal Cupola = (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)*sqrt(1-(1/4*cosec(pi/5)^(2)))

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