Edge Length of Dodecahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Edge Length of Dodecahedron = (2*Insphere Radius of Dodecahedron)/sqrt((25+(11*sqrt(5)))/10)
le = (2*ri)/sqrt((25+(11*sqrt(5)))/10)
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.
Insphere Radius of Dodecahedron - (Measured in Meter) - Insphere Radius of Dodecahedron is the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere.
STEP 1: Convert Input(s) to Base Unit
Insphere Radius of Dodecahedron: 11 Meter --> 11 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
le = (2*ri)/sqrt((25+(11*sqrt(5)))/10) --> (2*11)/sqrt((25+(11*sqrt(5)))/10)
Evaluating ... ...
le = 9.87861548475088
STEP 3: Convert Result to Output's Unit
9.87861548475088 Meter --> No Conversion Required
FINAL ANSWER
9.87861548475088 9.878615 Meter <-- Edge Length of Dodecahedron
(Calculation completed in 00.004 seconds)

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Mumbai University (DJSCE), Mumbai
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The National Institute of Engineering (NIE), Mysuru
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Edge Length of Dodecahedron Calculators

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

Edge Length of Dodecahedron Calculators

Edge Length of Dodecahedron given Total Surface Area
​ LaTeX ​ Go Edge Length of Dodecahedron = sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))
Edge Length of Dodecahedron given Insphere Radius
​ LaTeX ​ Go Edge Length of Dodecahedron = (2*Insphere Radius of Dodecahedron)/sqrt((25+(11*sqrt(5)))/10)
Edge Length of Dodecahedron given Circumsphere Radius
​ LaTeX ​ Go Edge Length of Dodecahedron = (4*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5)))
Edge Length of Dodecahedron given Volume
​ LaTeX ​ Go Edge Length of Dodecahedron = ((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)

Edge Length of Dodecahedron given Insphere Radius Formula

​LaTeX ​Go
Edge Length of Dodecahedron = (2*Insphere Radius of Dodecahedron)/sqrt((25+(11*sqrt(5)))/10)
le = (2*ri)/sqrt((25+(11*sqrt(5)))/10)

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 Insphere Radius?

Edge Length of Dodecahedron given Insphere Radius calculator uses Edge Length of Dodecahedron = (2*Insphere Radius of Dodecahedron)/sqrt((25+(11*sqrt(5)))/10) to calculate the Edge Length of Dodecahedron, The Edge Length of Dodecahedron given Insphere Radius 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 insphere radius of Dodecahedron. Edge Length of Dodecahedron is denoted by le symbol.

How to calculate Edge Length of Dodecahedron given Insphere Radius using this online calculator? To use this online calculator for Edge Length of Dodecahedron given Insphere Radius, enter Insphere Radius of Dodecahedron (ri) and hit the calculate button. Here is how the Edge Length of Dodecahedron given Insphere Radius calculation can be explained with given input values -> 9.878615 = (2*11)/sqrt((25+(11*sqrt(5)))/10).

FAQ

What is Edge Length of Dodecahedron given Insphere Radius?
The Edge Length of Dodecahedron given Insphere Radius 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 insphere radius of Dodecahedron and is represented as le = (2*ri)/sqrt((25+(11*sqrt(5)))/10) or Edge Length of Dodecahedron = (2*Insphere Radius of Dodecahedron)/sqrt((25+(11*sqrt(5)))/10). Insphere Radius of Dodecahedron is the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere.
How to calculate Edge Length of Dodecahedron given Insphere Radius?
The Edge Length of Dodecahedron given Insphere Radius 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 insphere radius of Dodecahedron is calculated using Edge Length of Dodecahedron = (2*Insphere Radius of Dodecahedron)/sqrt((25+(11*sqrt(5)))/10). To calculate Edge Length of Dodecahedron given Insphere Radius, you need Insphere Radius of Dodecahedron (ri). With our tool, you need to enter the respective value for Insphere Radius 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 Insphere Radius 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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