Edge Length of Great Dodecahedron given Surface to Volume Ratio Calculator

✖Surface to Volume Ratio of Great Dodecahedron is the numerical ratio of the total surface area of a Great Dodecahedron to the volume of the Great Dodecahedron.ⓘ Surface to Volume Ratio of Great Dodecahedron [R_A/V]

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✖Edge Length of Great Dodecahedron is the distance between any pair of adjacent peak vertices of the Great Dodecahedron.ⓘ Edge Length of Great Dodecahedron given Surface to Volume Ratio [l_e]

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Formula

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Edge Length of Great Dodecahedron given Surface to Volume Ratio

Formula

`"l"_{"e"} = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*"R"_{"A/V"})`

Example

`"10.07632m"=(15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*"0.7m⁻¹")`

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Edge Length of Great Dodecahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Edge Length of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Surface to Volume Ratio of Great Dodecahedron)
l_e = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*R_A/V)
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 Great Dodecahedron - (Measured in Meter) - Edge Length of Great Dodecahedron is the distance between any pair of adjacent peak vertices of the Great Dodecahedron.
Surface to Volume Ratio of Great Dodecahedron - (Measured in 1 per Meter) - Surface to Volume Ratio of Great Dodecahedron is the numerical ratio of the total surface area of a Great Dodecahedron to the volume of the Great Dodecahedron.

STEP 1: Convert Input(s) to Base Unit

Surface to Volume Ratio of Great Dodecahedron: 0.7 1 per Meter --> 0.7 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*R_A/V) --> (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*0.7)

Evaluating ... ...

l_e = 10.0763186107281

STEP 3: Convert Result to Output's Unit

10.0763186107281 Meter --> No Conversion Required

FINAL ANSWER

10.0763186107281 ≈ 10.07632 Meter <-- Edge Length of Great Dodecahedron

(Calculation completed in 00.005 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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Indian Institute of Information Technology (IIIT), Bhopal

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< 6 Edge Length of Great Dodecahedron Calculators

Edge Length of Great Dodecahedron given Surface to Volume Ratio

Go Edge Length of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Surface to Volume Ratio of Great Dodecahedron)

Edge Length of Great Dodecahedron given Total Surface Area

Go Edge Length of Great Dodecahedron = sqrt(Total Surface Area of Great Dodecahedron/(15*sqrt(5-(2*sqrt(5)))))

Edge Length of Great Dodecahedron given Circumsphere Radius

Go Edge Length of Great Dodecahedron = (4*Circumsphere Radius of Great Dodecahedron)/sqrt(10+(2*sqrt(5)))

Edge Length of Great Dodecahedron given Pyramidal Height

Go Edge Length of Great Dodecahedron = (6*Pyramidal Height of Great Dodecahedron)/(sqrt(3)*(3-sqrt(5)))

Edge Length of Great Dodecahedron given Volume

Go Edge Length of Great Dodecahedron = ((4*Volume of Great Dodecahedron)/(5*(sqrt(5)-1)))^(1/3)

Edge Length of Great Dodecahedron given Ridge Length

Go Edge Length of Great Dodecahedron = (2*Ridge Length of Great Dodecahedron)/(sqrt(5)-1)

Edge Length of Great Dodecahedron given Surface to Volume Ratio Formula

Edge Length of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Surface to Volume Ratio of Great Dodecahedron)
l_e = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*R_A/V)

What is Great Dodecahedron ?

The Great Dodecahedron is one of four nonconvex regular polyhedra. It is composed of 12 pentagonal faces, with five pentagons meeting at each vertex, intersecting each other making a pentagrammic path.

How to Calculate Edge Length of Great Dodecahedron given Surface to Volume Ratio?

Edge Length of Great Dodecahedron given Surface to Volume Ratio calculator uses Edge Length of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Surface to Volume Ratio of Great Dodecahedron) to calculate the Edge Length of Great Dodecahedron, Edge Length of Great Dodecahedron given Surface to Volume Ratio formula is defined as the distance between any pair of adjacent peak vertices of the Great Dodecahedron, calculated using its surface to volume ratio. Edge Length of Great Dodecahedron is denoted by l_e symbol.

How to calculate Edge Length of Great Dodecahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Edge Length of Great Dodecahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Great Dodecahedron (R_A/V) and hit the calculate button. Here is how the Edge Length of Great Dodecahedron given Surface to Volume Ratio calculation can be explained with given input values -> 10.07632 = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*0.7).

FAQ

What is Edge Length of Great Dodecahedron given Surface to Volume Ratio?

Edge Length of Great Dodecahedron given Surface to Volume Ratio formula is defined as the distance between any pair of adjacent peak vertices of the Great Dodecahedron, calculated using its surface to volume ratio and is represented as l_e = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*R_A/V) or Edge Length of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Surface to Volume Ratio of Great Dodecahedron). Surface to Volume Ratio of Great Dodecahedron is the numerical ratio of the total surface area of a Great Dodecahedron to the volume of the Great Dodecahedron.

How to calculate Edge Length of Great Dodecahedron given Surface to Volume Ratio?

Edge Length of Great Dodecahedron given Surface to Volume Ratio formula is defined as the distance between any pair of adjacent peak vertices of the Great Dodecahedron, calculated using its surface to volume ratio is calculated using Edge Length of Great Dodecahedron = (15*sqrt(5-(2*sqrt(5))))/(5/4*(sqrt(5)-1)*Surface to Volume Ratio of Great Dodecahedron). To calculate Edge Length of Great Dodecahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Great Dodecahedron (R_A/V). With our tool, you need to enter the respective value for Surface to Volume Ratio of Great Dodecahedron 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 Great Dodecahedron?

In this formula, Edge Length of Great Dodecahedron uses Surface to Volume Ratio of Great Dodecahedron. We can use 5 other way(s) to calculate the same, which is/are as follows -

Edge Length of Great Dodecahedron = (2*Ridge Length of Great Dodecahedron)/(sqrt(5)-1)
Edge Length of Great Dodecahedron = (4*Circumsphere Radius of Great Dodecahedron)/sqrt(10+(2*sqrt(5)))
Edge Length of Great Dodecahedron = (6*Pyramidal Height of Great Dodecahedron)/(sqrt(3)*(3-sqrt(5)))
Edge Length of Great Dodecahedron = sqrt(Total Surface Area of Great Dodecahedron/(15*sqrt(5-(2*sqrt(5)))))
Edge Length of Great Dodecahedron = ((4*Volume of Great Dodecahedron)/(5*(sqrt(5)-1)))^(1/3)

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