## Face Diagonal of Dodecahedron given Volume Solution

STEP 0: Pre-Calculation Summary
Formula Used
Face Diagonal of Dodecahedron = (1+sqrt(5))/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
dFace = (1+sqrt(5))/2*((4*V)/(15+(7*sqrt(5))))^(1/3)
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - Square root function, sqrt(Number)
Variables Used
Face Diagonal of Dodecahedron - (Measured in Meter) - The Face Diagonal of Dodecahedron is defined as the distance between any pair of opposite corners on a particular pentagonal face of the Dodecahedron.
Volume of Dodecahedron - (Measured in Cubic Meter) - Volume of Dodecahedron is the total quantity of three dimensional space enclosed by the surface of the Dodecahedron.
STEP 1: Convert Input(s) to Base Unit
Volume of Dodecahedron: 7700 Cubic Meter --> 7700 Cubic Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
dFace = (1+sqrt(5))/2*((4*V)/(15+(7*sqrt(5))))^(1/3) --> (1+sqrt(5))/2*((4*7700)/(15+(7*sqrt(5))))^(1/3)
Evaluating ... ...
dFace = 16.2062559218218
STEP 3: Convert Result to Output's Unit
16.2062559218218 Meter --> No Conversion Required
16.2062559218218 16.20626 Meter <-- Face Diagonal of Dodecahedron
(Calculation completed in 00.003 seconds)
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## < 12 Face Diagonal of Dodecahedron Calculators

Face Diagonal of Dodecahedron given Surface to Volume Ratio
Face Diagonal of Dodecahedron = (1+sqrt(5))*(6*sqrt(25+(10*sqrt(5))))/((15+(7*sqrt(5)))*Surface to Volume Ratio of Dodecahedron)
Face Diagonal of Dodecahedron given Lateral Surface Area
Face Diagonal of Dodecahedron = (1+sqrt(5))/2* sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5)))))
Face Diagonal of Dodecahedron given Total Surface Area
Face Diagonal of Dodecahedron = (1+sqrt(5))/2*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))
Face Diagonal of Dodecahedron given Face Area
Face Diagonal of Dodecahedron = (1+sqrt(5))/2*sqrt((4*Face Area of Dodecahedron)/(sqrt(25+(10*sqrt(5)))))
Face Diagonal of Dodecahedron given Insphere Radius
Face Diagonal of Dodecahedron = (1+sqrt(5))*Insphere Radius of Dodecahedron/sqrt((25+(11*sqrt(5)))/10)
Face Diagonal of Dodecahedron given Volume
Face Diagonal of Dodecahedron = (1+sqrt(5))/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
Face Diagonal of Dodecahedron given Midsphere Radius
Face Diagonal of Dodecahedron = (2*(1+sqrt(5)))/(3+sqrt(5))*Midsphere Radius of Dodecahedron
Face Diagonal of Dodecahedron given Face Perimeter
Face Diagonal of Dodecahedron = (1+sqrt(5))/10*Face Perimeter of Dodecahedron
Face Diagonal of Dodecahedron given Circumsphere Radius
Face Diagonal of Dodecahedron = 2/sqrt(3)*Circumsphere Radius of Dodecahedron
Face Diagonal of Dodecahedron
Face Diagonal of Dodecahedron = ((1+sqrt(5))/2)*Edge Length of Dodecahedron
Face Diagonal of Dodecahedron given Perimeter
Face Diagonal of Dodecahedron = (1+sqrt(5))/60*Perimeter of Dodecahedron
Face Diagonal of Dodecahedron given Space Diagonal
Face Diagonal of Dodecahedron = Space Diagonal of Dodecahedron/sqrt(3)

## Face Diagonal of Dodecahedron given Volume Formula

Face Diagonal of Dodecahedron = (1+sqrt(5))/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
dFace = (1+sqrt(5))/2*((4*V)/(15+(7*sqrt(5))))^(1/3)

## 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 Face Diagonal of Dodecahedron given Volume?

Face Diagonal of Dodecahedron given Volume calculator uses Face Diagonal of Dodecahedron = (1+sqrt(5))/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3) to calculate the Face Diagonal of Dodecahedron, The Face Diagonal of Dodecahedron given Volume formula is defined as the distance between any pair of opposite corners on a particular pentagonal face of the Dodecahedron, and calculated using volume of Dodecahedron. Face Diagonal of Dodecahedron is denoted by dFace symbol.

How to calculate Face Diagonal of Dodecahedron given Volume using this online calculator? To use this online calculator for Face Diagonal of Dodecahedron given Volume, enter Volume of Dodecahedron (V) and hit the calculate button. Here is how the Face Diagonal of Dodecahedron given Volume calculation can be explained with given input values -> 16.20626 = (1+sqrt(5))/2*((4*7700)/(15+(7*sqrt(5))))^(1/3).

### FAQ

What is Face Diagonal of Dodecahedron given Volume?
The Face Diagonal of Dodecahedron given Volume formula is defined as the distance between any pair of opposite corners on a particular pentagonal face of the Dodecahedron, and calculated using volume of Dodecahedron and is represented as dFace = (1+sqrt(5))/2*((4*V)/(15+(7*sqrt(5))))^(1/3) or Face Diagonal of Dodecahedron = (1+sqrt(5))/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3). Volume of Dodecahedron is the total quantity of three dimensional space enclosed by the surface of the Dodecahedron.
How to calculate Face Diagonal of Dodecahedron given Volume?
The Face Diagonal of Dodecahedron given Volume formula is defined as the distance between any pair of opposite corners on a particular pentagonal face of the Dodecahedron, and calculated using volume of Dodecahedron is calculated using Face Diagonal of Dodecahedron = (1+sqrt(5))/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3). To calculate Face Diagonal of Dodecahedron given Volume, you need Volume of Dodecahedron (V). With our tool, you need to enter the respective value for Volume 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 Face Diagonal of Dodecahedron?
In this formula, Face Diagonal of Dodecahedron uses Volume of Dodecahedron. We can use 11 other way(s) to calculate the same, which is/are as follows -
• Face Diagonal of Dodecahedron = ((1+sqrt(5))/2)*Edge Length of Dodecahedron
• Face Diagonal of Dodecahedron = (1+sqrt(5))/2*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))
• Face Diagonal of Dodecahedron = (1+sqrt(5))/2*sqrt((4*Face Area of Dodecahedron)/(sqrt(25+(10*sqrt(5)))))
• Face Diagonal of Dodecahedron = 2/sqrt(3)*Circumsphere Radius of Dodecahedron
• Face Diagonal of Dodecahedron = (1+sqrt(5))*Insphere Radius of Dodecahedron/sqrt((25+(11*sqrt(5)))/10)
• Face Diagonal of Dodecahedron = (1+sqrt(5))/10*Face Perimeter of Dodecahedron
• Face Diagonal of Dodecahedron = Space Diagonal of Dodecahedron/sqrt(3)
• Face Diagonal of Dodecahedron = (2*(1+sqrt(5)))/(3+sqrt(5))*Midsphere Radius of Dodecahedron
• Face Diagonal of Dodecahedron = (1+sqrt(5))*(6*sqrt(25+(10*sqrt(5))))/((15+(7*sqrt(5)))*Surface to Volume Ratio of Dodecahedron)
• Face Diagonal of Dodecahedron = (1+sqrt(5))/2* sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5)))))
• Face Diagonal of Dodecahedron = (1+sqrt(5))/60*Perimeter of Dodecahedron
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