## Edge Length of Dodecahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
Edge Length of Dodecahedron = (12*sqrt(25+(10*sqrt(5))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5))))
le = (12*sqrt(25+(10*sqrt(5))))/(RA/V*(15+(7*sqrt(5))))
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 Dodecahedron - (Measured in Meter) - Edge Length of Dodecahedron is the length of any of the edges of a Dodecahedron or the distance between any pair of adjacent vertices of the Dodecahedron.
Surface to Volume Ratio of Dodecahedron - (Measured in 1 per Meter) - The Surface to Volume Ratio of Dodecahedron is the numerical ratio of the total surface area to the volume of the Dodecahedron.
STEP 1: Convert Input(s) to Base Unit
Surface to Volume Ratio of Dodecahedron: 0.3 1 per Meter --> 0.3 1 per Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
le = (12*sqrt(25+(10*sqrt(5))))/(RA/V*(15+(7*sqrt(5)))) --> (12*sqrt(25+(10*sqrt(5))))/(0.3*(15+(7*sqrt(5))))
Evaluating ... ...
le = 8.98055953159171
STEP 3: Convert Result to Output's Unit
8.98055953159171 Meter --> No Conversion Required
8.98055953159171 8.98056 Meter <-- Edge Length of Dodecahedron
(Calculation completed in 00.004 seconds)
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## <Edge Length of Dodecahedron Calculators

Edge Length of Dodecahedron given Total Surface Area
​ Go Edge Length of Dodecahedron = sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))
Edge Length of Dodecahedron given Face Area
​ Go Edge Length of Dodecahedron = sqrt((4*Face Area of Dodecahedron)/sqrt(25+(10*sqrt(5))))
Edge Length of Dodecahedron given Circumsphere Radius
​ Go Edge Length of Dodecahedron = (4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5)))
Edge Length of Dodecahedron given Volume
​ Go Edge Length of Dodecahedron = ((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)

## Edge Length of Dodecahedron given Surface to Volume Ratio Formula

Edge Length of Dodecahedron = (12*sqrt(25+(10*sqrt(5))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5))))
le = (12*sqrt(25+(10*sqrt(5))))/(RA/V*(15+(7*sqrt(5))))

## What is a Dodecahedron?

A Dodecahedron is a symmetric and closed three dimensional shape with 12 identical pentagonal faces. It is a Platonic solid, which has 12 faces, 20 vertices and 30 edges. At each vertex, three pentagonal faces meet and at each edge, two pentagonal faces meet. Out of all the five Platonic solids with identical edge length, Dodecahedron will have the highest value of volume and surface area.

## What are Platonic Solids?

In three-dimensional space, a Platonic solid is a regular, convex polyhedron. It is constructed by congruent (identical in shape and size), regular (all angles equal and all sides equal), polygonal faces with the same number of faces meeting at each vertex. Five solids who meet this criteria are Tetrahedron {3,3} , Cube {4,3} , Octahedron {3,4} , Dodecahedron {5,3} , Icosahedron {3,5} ; where in {p, q}, p represents the number of edges in a face and q represents the number of edges meeting at a vertex; {p, q} is the Schläfli symbol.

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

Edge Length of Dodecahedron given Surface to Volume Ratio calculator uses Edge Length of Dodecahedron = (12*sqrt(25+(10*sqrt(5))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5)))) to calculate the Edge Length of Dodecahedron, The Edge Length of Dodecahedron given Surface to Volume Ratio formula is defined as the length of any of the edges of a Dodecahedron or the distance between any pair of adjacent vertices of the Dodecahedron, and calculated using surface to volume ratio of Dodecahedron. Edge Length of Dodecahedron is denoted by le symbol.

How to calculate Edge Length of Dodecahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Edge Length of Dodecahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Dodecahedron (RA/V) and hit the calculate button. Here is how the Edge Length of Dodecahedron given Surface to Volume Ratio calculation can be explained with given input values -> 8.98056 = (12*sqrt(25+(10*sqrt(5))))/(0.3*(15+(7*sqrt(5)))).

### FAQ

What is Edge Length of Dodecahedron given Surface to Volume Ratio?
The Edge Length of Dodecahedron given Surface to Volume Ratio formula is defined as the length of any of the edges of a Dodecahedron or the distance between any pair of adjacent vertices of the Dodecahedron, and calculated using surface to volume ratio of Dodecahedron and is represented as le = (12*sqrt(25+(10*sqrt(5))))/(RA/V*(15+(7*sqrt(5)))) or Edge Length of Dodecahedron = (12*sqrt(25+(10*sqrt(5))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5)))). The Surface to Volume Ratio of Dodecahedron is the numerical ratio of the total surface area to the volume of the Dodecahedron.
How to calculate Edge Length of Dodecahedron given Surface to Volume Ratio?
The Edge Length of Dodecahedron given Surface to Volume Ratio formula is defined as the length of any of the edges of a Dodecahedron or the distance between any pair of adjacent vertices of the Dodecahedron, and calculated using surface to volume ratio of Dodecahedron is calculated using Edge Length of Dodecahedron = (12*sqrt(25+(10*sqrt(5))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5)))). To calculate Edge Length of Dodecahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Dodecahedron (RA/V). With our tool, you need to enter the respective value for Surface to Volume Ratio of 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 Dodecahedron?
In this formula, Edge Length of Dodecahedron uses Surface to Volume Ratio of Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -
• Edge Length of Dodecahedron = (4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5)))
• Edge Length of Dodecahedron = sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))
• Edge Length of Dodecahedron = ((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
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