Insphere Radius of Dodecahedron given Space Diagonal Solution

STEP 0: Pre-Calculation Summary
Formula Used
Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*Space Diagonal of Dodecahedron/(sqrt(3)*(1+sqrt(5)))
ri = sqrt((25+(11*sqrt(5)))/10)*dSpace/(sqrt(3)*(1+sqrt(5)))
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
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.
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.
STEP 1: Convert Input(s) to Base Unit
Space Diagonal of Dodecahedron: 28 Meter --> 28 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ri = sqrt((25+(11*sqrt(5)))/10)*dSpace/(sqrt(3)*(1+sqrt(5))) --> sqrt((25+(11*sqrt(5)))/10)*28/(sqrt(3)*(1+sqrt(5)))
Evaluating ... ...
ri = 11.1251626120847
STEP 3: Convert Result to Output's Unit
11.1251626120847 Meter --> No Conversion Required
FINAL ANSWER
11.1251626120847 11.12516 Meter <-- Insphere Radius of Dodecahedron
(Calculation completed in 00.004 seconds)

Credits

Created by Nikhil
Mumbai University (DJSCE), Mumbai
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12 Insphere Radius of Dodecahedron Calculators

Insphere Radius of Dodecahedron given Surface to Volume Ratio
Go 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
Go 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 Circumsphere Radius
Go Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*(2*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5)))
Insphere Radius of Dodecahedron given Total Surface Area
Go 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
Go 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
Go 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
Go 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 Midsphere Radius
Go Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*(2*Midsphere Radius of Dodecahedron)/(3+sqrt(5))
Insphere Radius of Dodecahedron given Face Diagonal
Go Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*Face Diagonal of Dodecahedron/(1+sqrt(5))
Insphere Radius of Dodecahedron given Face Perimeter
Go Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*Face Perimeter of Dodecahedron/10
Insphere Radius of Dodecahedron
Go Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*Edge Length of Dodecahedron/2
Insphere Radius of Dodecahedron given Perimeter
Go Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*Perimeter of Dodecahedron/60

Insphere Radius of Dodecahedron given Space Diagonal Formula

Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*Space Diagonal of Dodecahedron/(sqrt(3)*(1+sqrt(5)))
ri = sqrt((25+(11*sqrt(5)))/10)*dSpace/(sqrt(3)*(1+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 Insphere Radius of Dodecahedron given Space Diagonal?

Insphere Radius of Dodecahedron given Space Diagonal calculator uses Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*Space Diagonal of Dodecahedron/(sqrt(3)*(1+sqrt(5))) to calculate the Insphere Radius of Dodecahedron, The Insphere Radius of Dodecahedron given Space Diagonal 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 space diagonal of Dodecahedron. Insphere Radius of Dodecahedron is denoted by ri symbol.

How to calculate Insphere Radius of Dodecahedron given Space Diagonal using this online calculator? To use this online calculator for Insphere Radius of Dodecahedron given Space Diagonal, enter Space Diagonal of Dodecahedron (dSpace) and hit the calculate button. Here is how the Insphere Radius of Dodecahedron given Space Diagonal calculation can be explained with given input values -> 11.12516 = sqrt((25+(11*sqrt(5)))/10)*28/(sqrt(3)*(1+sqrt(5))).

FAQ

What is Insphere Radius of Dodecahedron given Space Diagonal?
The Insphere Radius of Dodecahedron given Space Diagonal 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 space diagonal of Dodecahedron and is represented as ri = sqrt((25+(11*sqrt(5)))/10)*dSpace/(sqrt(3)*(1+sqrt(5))) or Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*Space Diagonal of Dodecahedron/(sqrt(3)*(1+sqrt(5))). The Space Diagonal of Dodecahedron is the line connecting two vertices that are not on the same face of Dodecahedron.
How to calculate Insphere Radius of Dodecahedron given Space Diagonal?
The Insphere Radius of Dodecahedron given Space Diagonal 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 space diagonal of Dodecahedron is calculated using Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*Space Diagonal of Dodecahedron/(sqrt(3)*(1+sqrt(5))). To calculate Insphere Radius of Dodecahedron given Space Diagonal, you need Space Diagonal of Dodecahedron (dSpace). With our tool, you need to enter the respective value for Space Diagonal 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 Space Diagonal 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 = 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
  • Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*(2*Circumsphere Radius of Dodecahedron)/(sqrt(3)*(1+sqrt(5)))
  • Insphere Radius of Dodecahedron = sqrt((25+(11*sqrt(5)))/10)*(2*Midsphere Radius of Dodecahedron)/(3+sqrt(5))
  • 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 = sqrt((25+(11*sqrt(5)))/10)*Face Diagonal of Dodecahedron/(1+sqrt(5))
  • 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 = sqrt((25+(11*sqrt(5)))/10)*Perimeter of Dodecahedron/60
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