Space Diagonal of Dodecahedron given Volume Solution

STEP 0: Pre-Calculation Summary
Formula Used
Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
dSpace = sqrt(3)*(1+sqrt(5))/2*((4*V)/(15+(7*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
Space Diagonal of Dodecahedron - (Measured in Meter) - The Space Diagonal of Dodecahedron is the line connecting two vertices that are not on the same face of 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
dSpace = sqrt(3)*(1+sqrt(5))/2*((4*V)/(15+(7*sqrt(5))))^(1/3) --> sqrt(3)*(1+sqrt(5))/2*((4*7700)/(15+(7*sqrt(5))))^(1/3)
Evaluating ... ...
dSpace = 28.0700586570594
STEP 3: Convert Result to Output's Unit
28.0700586570594 Meter --> No Conversion Required
FINAL ANSWER
28.0700586570594 28.07006 Meter <-- Space Diagonal of Dodecahedron
(Calculation completed in 00.004 seconds)

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Space Diagonal of Dodecahedron Calculators

Space Diagonal of Dodecahedron given Total Surface Area
​ LaTeX ​ Go Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))
Space Diagonal of Dodecahedron given Face Area
​ LaTeX ​ Go Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*sqrt((12*Face Area of Dodecahedron)/(3*sqrt(25+(10*sqrt(5)))))
Space Diagonal of Dodecahedron given Volume
​ LaTeX ​ Go Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
Space Diagonal of Dodecahedron
​ LaTeX ​ Go Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*Edge Length of Dodecahedron/2

Space Diagonal of Dodecahedron given Volume Formula

​LaTeX ​Go
Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
dSpace = sqrt(3)*(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 Space Diagonal of Dodecahedron given Volume?

Space Diagonal of Dodecahedron given Volume calculator uses Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3) to calculate the Space Diagonal of Dodecahedron, The Space Diagonal of Dodecahedron given Volume formula is defined as a line connecting two vertices that are not on the same face of Dodecahedron, and calculated using volume of Dodecahedron. Space Diagonal of Dodecahedron is denoted by dSpace symbol.

How to calculate Space Diagonal of Dodecahedron given Volume using this online calculator? To use this online calculator for Space Diagonal of Dodecahedron given Volume, enter Volume of Dodecahedron (V) and hit the calculate button. Here is how the Space Diagonal of Dodecahedron given Volume calculation can be explained with given input values -> 28.07006 = sqrt(3)*(1+sqrt(5))/2*((4*7700)/(15+(7*sqrt(5))))^(1/3).

FAQ

What is Space Diagonal of Dodecahedron given Volume?
The Space Diagonal of Dodecahedron given Volume formula is defined as a line connecting two vertices that are not on the same face of Dodecahedron, and calculated using volume of Dodecahedron and is represented as dSpace = sqrt(3)*(1+sqrt(5))/2*((4*V)/(15+(7*sqrt(5))))^(1/3) or Space Diagonal of Dodecahedron = sqrt(3)*(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 Space Diagonal of Dodecahedron given Volume?
The Space Diagonal of Dodecahedron given Volume formula is defined as a line connecting two vertices that are not on the same face of Dodecahedron, and calculated using volume of Dodecahedron is calculated using Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3). To calculate Space 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 Space Diagonal of Dodecahedron?
In this formula, Space Diagonal of Dodecahedron uses Volume of Dodecahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))*Edge Length of Dodecahedron/2
  • Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))
  • Space Diagonal of Dodecahedron = sqrt(3)*(1+sqrt(5))/2*sqrt((12*Face Area of Dodecahedron)/(3*sqrt(25+(10*sqrt(5)))))
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