Face Perimeter of Dodecahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Face Perimeter of Dodecahedron = (20*Midsphere Radius of Dodecahedron)/(3+sqrt(5))
PFace = (20*rm)/(3+sqrt(5))
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Face Perimeter of Dodecahedron - (Measured in Meter) - Face Perimeter of Dodecahedron is the total distance around the five edges of any face of the Dodecahedron.
Midsphere Radius of Dodecahedron - (Measured in Meter) - The Midsphere Radius of Dodecahedron is defined as radius of the sphere for which all the edges of the Dodecahedron become a tangent line on that sphere.
STEP 1: Convert Input(s) to Base Unit
Midsphere Radius of Dodecahedron: 13 Meter --> 13 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
PFace = (20*rm)/(3+sqrt(5)) --> (20*13)/(3+sqrt(5))
Evaluating ... ...
PFace = 49.6555814625137
STEP 3: Convert Result to Output's Unit
49.6555814625137 Meter --> No Conversion Required
FINAL ANSWER
49.6555814625137 Meter <-- Face Perimeter of Dodecahedron
(Calculation completed in 00.009 seconds)

Credits

Created by Nikita Kumari
The National Institute of Engineering (NIE), Mysuru
Nikita Kumari has created this Calculator and 0 more calculators!
Verified by Nikhil
Mumbai University (DJSCE), Mumbai
Nikhil has verified this Calculator and 0 more calculators!

10+ Face Perimeter of Dodecahedron Calculators

Face Perimeter of Dodecahedron given Surface to Volume Ratio
Face Perimeter of Dodecahedron = (60*(sqrt(25+10*sqrt(5))))/(Surface to Volume Ratio of Dodecahedron*(15+7*sqrt(5))) Go
Face Perimeter of Dodecahedron given Total Surface Area
Face Perimeter of Dodecahedron = 5*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+10*sqrt(5)))) Go
Face Perimeter of Dodecahedron given Face Area
Face Perimeter of Dodecahedron = 5*sqrt((4*Face Area of Dodecahedron)/(sqrt(25+10*sqrt(5)))) Go
Face Perimeter of Dodecahedron given Insphere Radius
Face Perimeter of Dodecahedron = (10*Insphere Radius of Dodecahedron)/(sqrt((25+11*sqrt(5))/10)) Go
Face Perimeter of Dodecahedron given Circumsphere Radius
Face Perimeter of Dodecahedron = (20*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5))) Go
Face Perimeter of Dodecahedron given Space Diagonal
Face Perimeter of Dodecahedron = (10*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5))) Go
Face Perimeter of Dodecahedron given Volume
Face Perimeter of Dodecahedron = 5*((4*Volume of Dodecahedron)/(15+7*sqrt(5)))^(1/3) Go
Face Perimeter of Dodecahedron given Midsphere Radius
Face Perimeter of Dodecahedron = (20*Midsphere Radius of Dodecahedron)/(3+sqrt(5)) Go
Face Perimeter of Dodecahedron given Face Diagonal
Face Perimeter of Dodecahedron = (10*Face Diagonal of Dodecahedron)/(1+sqrt(5)) Go
Face Perimeter of Dodecahedron
Face Perimeter of Dodecahedron = 5*Edge Length of Dodecahedron Go

Face Perimeter of Dodecahedron given Midsphere Radius Formula

Face Perimeter of Dodecahedron = (20*Midsphere Radius of Dodecahedron)/(3+sqrt(5))
PFace = (20*rm)/(3+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 Face Perimeter of Dodecahedron given Midsphere Radius?

Face Perimeter of Dodecahedron given Midsphere Radius calculator uses Face Perimeter of Dodecahedron = (20*Midsphere Radius of Dodecahedron)/(3+sqrt(5)) to calculate the Face Perimeter of Dodecahedron, The Face Perimeter of Dodecahedron given Midsphere Radius formula is defined as the total distance around the five edges of any face of the Dodecahedron, and calculated using the midsphere radius of Dodecahedron. Face Perimeter of Dodecahedron is denoted by PFace symbol.

How to calculate Face Perimeter of Dodecahedron given Midsphere Radius using this online calculator? To use this online calculator for Face Perimeter of Dodecahedron given Midsphere Radius, enter Midsphere Radius of Dodecahedron (rm) and hit the calculate button. Here is how the Face Perimeter of Dodecahedron given Midsphere Radius calculation can be explained with given input values -> 49.65558 = (20*13)/(3+sqrt(5)).

FAQ

What is Face Perimeter of Dodecahedron given Midsphere Radius?
The Face Perimeter of Dodecahedron given Midsphere Radius formula is defined as the total distance around the five edges of any face of the Dodecahedron, and calculated using the midsphere radius of Dodecahedron and is represented as PFace = (20*rm)/(3+sqrt(5)) or Face Perimeter of Dodecahedron = (20*Midsphere Radius of Dodecahedron)/(3+sqrt(5)). The Midsphere Radius of Dodecahedron is defined as radius of the sphere for which all the edges of the Dodecahedron become a tangent line on that sphere.
How to calculate Face Perimeter of Dodecahedron given Midsphere Radius?
The Face Perimeter of Dodecahedron given Midsphere Radius formula is defined as the total distance around the five edges of any face of the Dodecahedron, and calculated using the midsphere radius of Dodecahedron is calculated using Face Perimeter of Dodecahedron = (20*Midsphere Radius of Dodecahedron)/(3+sqrt(5)). To calculate Face Perimeter of Dodecahedron given Midsphere Radius, you need Midsphere Radius of Dodecahedron (rm). With our tool, you need to enter the respective value for Midsphere 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 Face Perimeter of Dodecahedron?
In this formula, Face Perimeter of Dodecahedron uses Midsphere Radius of Dodecahedron. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • Face Perimeter of Dodecahedron = 5*Edge Length of Dodecahedron
  • Face Perimeter of Dodecahedron = 5*sqrt((4*Face Area of Dodecahedron)/(sqrt(25+10*sqrt(5))))
  • Face Perimeter of Dodecahedron = 5*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+10*sqrt(5))))
  • Face Perimeter of Dodecahedron = (20*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5)))
  • Face Perimeter of Dodecahedron = 5*((4*Volume of Dodecahedron)/(15+7*sqrt(5)))^(1/3)
  • Face Perimeter of Dodecahedron = (10*Space Diagonal of Dodecahedron)/(sqrt(3)*(1+sqrt(5)))
  • Face Perimeter of Dodecahedron = (10*Insphere Radius of Dodecahedron)/(sqrt((25+11*sqrt(5))/10))
  • Face Perimeter of Dodecahedron = (10*Face Diagonal of Dodecahedron)/(1+sqrt(5))
  • Face Perimeter of Dodecahedron = (60*(sqrt(25+10*sqrt(5))))/(Surface to Volume Ratio of Dodecahedron*(15+7*sqrt(5)))
  • Face Perimeter of Dodecahedron = sqrt((10*Lateral Surface Area of Dodecahedron)/sqrt(25+10*sqrt(5)))
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