## Insphere Radius of Dodecahedron given Perimeter Solution

STEP 0: Pre-Calculation Summary
Formula Used
Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*Perimeter of Dodecahedron/60
ri = sqrt((25+(11*sqrt(5)))/10)*P/60
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
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.
Perimeter of Dodecahedron - (Measured in Meter) - Perimeter of Dodecahedron is the sum of the total distance around all the edges of the Dodecahedron.
STEP 1: Convert Input(s) to Base Unit
Perimeter of Dodecahedron: 300 Meter --> 300 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ri = sqrt((25+(11*sqrt(5)))/10)*P/60 --> sqrt((25+(11*sqrt(5)))/10)*300/60
Evaluating ... ...
ri = 11.1351636441161
STEP 3: Convert Result to Output's Unit
11.1351636441161 Meter --> No Conversion Required
11.1351636441161 Meter <-- Insphere Radius of Dodecahedron
(Calculation completed in 00.004 seconds)
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## Credits

Created by Dhruv Walia
Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
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## < 12 Insphere Radius of Dodecahedron Calculators

Insphere Radius of Dodecahedron given Surface to Volume Ratio
Insphere Radius of Dodecahedron = ((6*sqrt(25+10*sqrt(5)))/(Surface to Volume Ratio of Dodecahedron*(15+7*sqrt(5))))*sqrt((25+11*sqrt(5))/10)
Insphere Radius of Dodecahedron given Lateral Surface Area
Insphere Radius of Dodecahedron = sqrt((25+11*sqrt(5))/10)*sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+10*sqrt(5))))/2
Insphere Radius of Dodecahedron given Total Surface Area
Insphere Radius of Dodecahedron = sqrt((Total Surface Area of Dodecahedron*(25+11*sqrt(5)))/(30*sqrt(25+10*sqrt(5))))/2
Insphere Radius of Dodecahedron given Space Diagonal
Insphere Radius of Dodecahedron = (Space Diagonal of Dodecahedron/(sqrt(3)*(1+sqrt(5))))*sqrt((25+11*sqrt(5))/10)
Insphere Radius of Dodecahedron given Face Area
Insphere Radius of Dodecahedron = sqrt((2*Face Area of Dodecahedron*(25+11*sqrt(5)))/(5*sqrt(25+10*sqrt(5))))/2
Insphere Radius of Dodecahedron given Volume
Insphere Radius of Dodecahedron = ((4*Volume of Dodecahedron)/(15+7*sqrt(5)))^(1/3)*sqrt((25+11*sqrt(5))/10)/2
Insphere Radius of Dodecahedron given Face Diagonal
Insphere Radius of Dodecahedron = (Face Diagonal of Dodecahedron/(1+sqrt(5)))*sqrt((25+11*sqrt(5))/10)
Insphere Radius of Dodecahedron given Face Perimeter
Insphere Radius of Dodecahedron = (sqrt((25+(11*sqrt(5)))/10))*(Face Perimeter of Dodecahedron/10)
Insphere Radius of Dodecahedron = (sqrt((25+(11*sqrt(5)))/10))*(Edge Length of Dodecahedron/2)
Insphere Radius of Dodecahedron given Perimeter
Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*Perimeter of Dodecahedron/60

## Insphere Radius of Dodecahedron given Perimeter Formula

Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*Perimeter of Dodecahedron/60
ri = sqrt((25+(11*sqrt(5)))/10)*P/60

## 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 Insphere Radius of Dodecahedron given Perimeter?

Insphere Radius of Dodecahedron given Perimeter calculator uses Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*Perimeter of Dodecahedron/60 to calculate the Insphere Radius of Dodecahedron, The Insphere Radius of Dodecahedron given Perimeter formula is defined as the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere, and calculated using the perimeter of the Dodecahedron. Insphere Radius of Dodecahedron is denoted by ri symbol.

How to calculate Insphere Radius of Dodecahedron given Perimeter using this online calculator? To use this online calculator for Insphere Radius of Dodecahedron given Perimeter, enter Perimeter of Dodecahedron (P) and hit the calculate button. Here is how the Insphere Radius of Dodecahedron given Perimeter calculation can be explained with given input values -> 11.13516 = sqrt((25+(11*sqrt(5)))/10)*300/60.

### FAQ

What is Insphere Radius of Dodecahedron given Perimeter?
The Insphere Radius of Dodecahedron given Perimeter formula is defined as the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere, and calculated using the perimeter of the Dodecahedron and is represented as ri = sqrt((25+(11*sqrt(5)))/10)*P/60 or Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*Perimeter of Dodecahedron/60. Perimeter of Dodecahedron is the sum of the total distance around all the edges of the Dodecahedron.
How to calculate Insphere Radius of Dodecahedron given Perimeter?
The Insphere Radius of Dodecahedron given Perimeter formula is defined as the radius of the sphere that is contained by the Dodecahedron in such a way that all the faces just touching the sphere, and calculated using the perimeter of the Dodecahedron is calculated using Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*Perimeter of Dodecahedron/60. To calculate Insphere Radius of Dodecahedron given Perimeter, you need Perimeter of Dodecahedron (P). With our tool, you need to enter the respective value for Perimeter 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 Insphere Radius of Dodecahedron?
In this formula, Insphere Radius of Dodecahedron uses Perimeter of Dodecahedron. We can use 11 other way(s) to calculate the same, which is/are as follows -
• Insphere Radius of Dodecahedron = (sqrt((25+(11*sqrt(5)))/10))*(Edge Length of Dodecahedron/2)
• Insphere Radius of Dodecahedron = ((4*Volume of Dodecahedron)/(15+7*sqrt(5)))^(1/3)*sqrt((25+11*sqrt(5))/10)/2
• Insphere Radius of Dodecahedron = sqrt((Total Surface Area of Dodecahedron*(25+11*sqrt(5)))/(30*sqrt(25+10*sqrt(5))))/2
• Insphere Radius of Dodecahedron = sqrt((2*Face Area of Dodecahedron*(25+11*sqrt(5)))/(5*sqrt(25+10*sqrt(5))))/2
• Insphere Radius of Dodecahedron = (sqrt((25+(11*sqrt(5)))/10))*(Face Perimeter of Dodecahedron/10)