Edge Length 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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✖Edge Length of Pentagonal Cupola is the length of any edge of the Pentagonal Cupola.ⓘ Edge Length of Pentagonal Cupola given Volume [l_e]

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Edge Length of Pentagonal Cupola given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Edge Length of Pentagonal Cupola = (Volume of Pentagonal Cupola/(1/6*(5+(4*sqrt(5)))))^(1/3)
l_e = (V/(1/6*(5+(4*sqrt(5)))))^(1/3)
This formula uses 1 Functions, 2 Variables

Functions Used

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

Edge Length of Pentagonal Cupola - (Measured in Meter) - Edge Length of Pentagonal Cupola is the length of any edge 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

l_e = (V/(1/6*(5+(4*sqrt(5)))))^(1/3) --> (2300/(1/6*(5+(4*sqrt(5)))))^(1/3)

Evaluating ... ...

l_e = 9.96539263531208

STEP 3: Convert Result to Output's Unit

9.96539263531208 Meter --> No Conversion Required

FINAL ANSWER

9.96539263531208 ≈ 9.965393 Meter <-- Edge Length of Pentagonal Cupola

(Calculation completed in 00.004 seconds)

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< Edge Length of Pentagonal Cupola Calculators

Edge Length of Pentagonal Cupola given Surface to Volume Ratio

LaTeX Go Edge Length 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)

Edge Length of Pentagonal Cupola given Total Surface Area

LaTeX Go Edge Length of Pentagonal Cupola = sqrt(Total Surface Area of Pentagonal Cupola/(1/4*(20+(5*sqrt(3))+sqrt(5*(145+(62*sqrt(5)))))))

Edge Length of Pentagonal Cupola given Height

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

Edge Length of Pentagonal Cupola given Volume

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

Edge Length of Pentagonal Cupola given Volume Formula

LaTeX Go

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

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 Edge Length of Pentagonal Cupola given Volume?

Edge Length of Pentagonal Cupola given Volume calculator uses Edge Length of Pentagonal Cupola = (Volume of Pentagonal Cupola/(1/6*(5+(4*sqrt(5)))))^(1/3) to calculate the Edge Length of Pentagonal Cupola, The Edge Length of Pentagonal Cupola given Volume formula is defined as the length of any edge of the Pentagonal Cupola and is calculated using the volume of the Pentagonal Cupola. Edge Length of Pentagonal Cupola is denoted by l_e symbol.

How to calculate Edge Length of Pentagonal Cupola given Volume using this online calculator? To use this online calculator for Edge Length of Pentagonal Cupola given Volume, enter Volume of Pentagonal Cupola (V) and hit the calculate button. Here is how the Edge Length of Pentagonal Cupola given Volume calculation can be explained with given input values -> 9.965393 = (2300/(1/6*(5+(4*sqrt(5)))))^(1/3).

FAQ

What is Edge Length of Pentagonal Cupola given Volume?

The Edge Length of Pentagonal Cupola given Volume formula is defined as the length of any edge of the Pentagonal Cupola and is calculated using the volume of the Pentagonal Cupola and is represented as l_e = (V/(1/6*(5+(4*sqrt(5)))))^(1/3) or Edge Length of Pentagonal Cupola = (Volume of Pentagonal Cupola/(1/6*(5+(4*sqrt(5)))))^(1/3). Volume of Pentagonal Cupola is the total quantity of three-dimensional space enclosed by the surface of the Pentagonal Cupola.

How to calculate Edge Length of Pentagonal Cupola given Volume?

The Edge Length of Pentagonal Cupola given Volume formula is defined as the length of any edge of the Pentagonal Cupola and is calculated using the volume of the Pentagonal Cupola is calculated using Edge Length of Pentagonal Cupola = (Volume of Pentagonal Cupola/(1/6*(5+(4*sqrt(5)))))^(1/3). To calculate Edge Length 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 Edge Length of Pentagonal Cupola?

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

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

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