## Insphere Radius of Dodecahedron Solution

STEP 0: Pre-Calculation Summary
Formula Used
Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*Edge Length of Dodecahedron/2
ri = sqrt((25+(11*sqrt(5)))/10)*le/2
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - Square 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.
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.
STEP 1: Convert Input(s) to Base Unit
Edge Length of Dodecahedron: 10 Meter --> 10 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ri = sqrt((25+(11*sqrt(5)))/10)*le/2 --> sqrt((25+(11*sqrt(5)))/10)*10/2
Evaluating ... ...
ri = 11.1351636441161
STEP 3: Convert Result to Output's Unit
11.1351636441161 Meter --> No Conversion Required
11.1351636441161 11.13516 Meter <-- Insphere Radius of Dodecahedron
(Calculation completed in 00.004 seconds)
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## < 12 Insphere Radius of Dodecahedron Calculators

Insphere Radius of Dodecahedron given Surface to Volume Ratio
Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*(6*sqrt(25+(10*sqrt(5))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5))))
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))))/(120*sqrt(25+(10*sqrt(5)))))
Insphere Radius of Dodecahedron given Space Diagonal
Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*Space Diagonal of Dodecahedron/(sqrt(3)*(1+sqrt(5)))
Insphere Radius of Dodecahedron given Face Area
Insphere Radius of Dodecahedron = sqrt((Face Area of Dodecahedron*(25+(11*sqrt(5))))/(10*sqrt(25+(10*sqrt(5)))))
Insphere Radius of Dodecahedron given Volume
Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
Insphere Radius of Dodecahedron given Face Diagonal
Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*Face Diagonal of Dodecahedron/(1+sqrt(5))
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

## < 6 Radius of Dodecahedron Calculators

Circumsphere Radius of Dodecahedron given Total Surface Area
Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))/4*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))
Midsphere Radius of Dodecahedron given Lateral Surface Area
Midsphere Radius of Dodecahedron = (3+sqrt(5))/4*sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5)))))
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
Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))*Edge Length of Dodecahedron/4
Midsphere Radius of Dodecahedron = (3+sqrt(5))/4*Edge Length of Dodecahedron

## Insphere Radius of Dodecahedron Formula

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

## 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?

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

How to calculate Insphere Radius of Dodecahedron using this online calculator? To use this online calculator for Insphere Radius of Dodecahedron, enter Edge Length of Dodecahedron (le) and hit the calculate button. Here is how the Insphere Radius of Dodecahedron calculation can be explained with given input values -> 11.13516 = sqrt((25+(11*sqrt(5)))/10)*10/2.

### FAQ

What is Insphere Radius of Dodecahedron?
Insphere Radius of Dodecahedron 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 is represented as ri = sqrt((25+(11*sqrt(5)))/10)*le/2 or Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*Edge Length of Dodecahedron/2. 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.
How to calculate Insphere Radius of Dodecahedron?
Insphere Radius of Dodecahedron 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 is calculated using Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*Edge Length of Dodecahedron/2. To calculate Insphere Radius of Dodecahedron, you need Edge Length of Dodecahedron (le). With our tool, you need to enter the respective value for Edge Length 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 Edge Length of Dodecahedron. We can use 12 other way(s) to calculate the same, which is/are as follows -
• Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)/2*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
• Insphere Radius of Dodecahedron = sqrt((Total Surface Area of Dodecahedron*(25+(11*sqrt(5))))/(120*sqrt(25+(10*sqrt(5)))))
• Insphere Radius of Dodecahedron = sqrt((Face Area of Dodecahedron*(25+(11*sqrt(5))))/(10*sqrt(25+(10*sqrt(5)))))
• Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*Face Perimeter of Dodecahedron/10