Midsphere Radius of Dodecahedron given Perimeter Solution

STEP 0: Pre-Calculation Summary
Formula Used
Midsphere Radius of Dodecahedron = (3+sqrt(5))/120*Perimeter of Dodecahedron
rm = (3+sqrt(5))/120*P
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
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.
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
rm = (3+sqrt(5))/120*P --> (3+sqrt(5))/120*300
Evaluating ... ...
rm = 13.0901699437495
STEP 3: Convert Result to Output's Unit
13.0901699437495 Meter --> No Conversion Required
FINAL ANSWER
13.0901699437495 13.09017 Meter <-- Midsphere Radius of Dodecahedron
(Calculation completed in 00.020 seconds)

Credits

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

Midsphere Radius of Dodecahedron given Surface to Volume Ratio
Go Midsphere Radius of Dodecahedron = (3+sqrt(5))*(3*sqrt(25+(10*sqrt(5))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5))))
Midsphere Radius of Dodecahedron given Lateral Surface Area
Go Midsphere Radius of Dodecahedron = (3+sqrt(5))/4*sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5)))))
Midsphere Radius of Dodecahedron given Total Surface Area
Go Midsphere Radius of Dodecahedron = (3+sqrt(5))/4*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))
Midsphere Radius of Dodecahedron given Face Area
Go Midsphere Radius of Dodecahedron = (3+sqrt(5))/4*sqrt((4*Face Area of Dodecahedron)/sqrt(25+(10*sqrt(5))))
Midsphere Radius of Dodecahedron given Insphere Radius
Go Midsphere Radius of Dodecahedron = (3+sqrt(5))/2*Insphere Radius of Dodecahedron/sqrt((25+(11*sqrt(5)))/10)
Midsphere Radius of Dodecahedron given Circumsphere Radius
Go Midsphere Radius of Dodecahedron = (3+sqrt(5))*Circumsphere Radius of Dodecahedron/(sqrt(3)*(1+sqrt(5)))
Midsphere Radius of Dodecahedron given Space Diagonal
Go Midsphere Radius of Dodecahedron = (3+sqrt(5))/2*Space Diagonal of Dodecahedron/(sqrt(3)*(1+sqrt(5)))
Midsphere Radius of Dodecahedron given Volume
Go Midsphere Radius of Dodecahedron = (3+sqrt(5))/4*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
Midsphere Radius of Dodecahedron given Face Diagonal
Go Midsphere Radius of Dodecahedron = (3+sqrt(5))/2*Face Diagonal of Dodecahedron/(1+sqrt(5))
Midsphere Radius of Dodecahedron given Face Perimeter
Go Midsphere Radius of Dodecahedron = (3+sqrt(5))/20*Face Perimeter of Dodecahedron
Midsphere Radius of Dodecahedron given Perimeter
Go Midsphere Radius of Dodecahedron = (3+sqrt(5))/120*Perimeter of Dodecahedron
Midsphere Radius of Dodecahedron
Go Midsphere Radius of Dodecahedron = (3+sqrt(5))/4*Edge Length of Dodecahedron

Midsphere Radius of Dodecahedron given Perimeter Formula

Midsphere Radius of Dodecahedron = (3+sqrt(5))/120*Perimeter of Dodecahedron
rm = (3+sqrt(5))/120*P

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 Midsphere Radius of Dodecahedron given Perimeter?

Midsphere Radius of Dodecahedron given Perimeter calculator uses Midsphere Radius of Dodecahedron = (3+sqrt(5))/120*Perimeter of Dodecahedron to calculate the Midsphere Radius of Dodecahedron, The Midsphere Radius of Dodecahedron given Perimeter formula is defined as the radius of the sphere for which all the edges of the Dodecahedron become a tangent line on that sphere, and calculated using the perimeter of the Dodecahedron. Midsphere Radius of Dodecahedron is denoted by rm symbol.

How to calculate Midsphere Radius of Dodecahedron given Perimeter using this online calculator? To use this online calculator for Midsphere Radius of Dodecahedron given Perimeter, enter Perimeter of Dodecahedron (P) and hit the calculate button. Here is how the Midsphere Radius of Dodecahedron given Perimeter calculation can be explained with given input values -> 13.09017 = (3+sqrt(5))/120*300.

FAQ

What is Midsphere Radius of Dodecahedron given Perimeter?
The Midsphere Radius of Dodecahedron given Perimeter formula is defined as the radius of the sphere for which all the edges of the Dodecahedron become a tangent line on that sphere, and calculated using the perimeter of the Dodecahedron and is represented as rm = (3+sqrt(5))/120*P or Midsphere Radius of Dodecahedron = (3+sqrt(5))/120*Perimeter of Dodecahedron. Perimeter of Dodecahedron is the sum of the total distance around all the edges of the Dodecahedron.
How to calculate Midsphere Radius of Dodecahedron given Perimeter?
The Midsphere Radius of Dodecahedron given Perimeter formula is defined as the radius of the sphere for which all the edges of the Dodecahedron become a tangent line on that sphere, and calculated using the perimeter of the Dodecahedron is calculated using Midsphere Radius of Dodecahedron = (3+sqrt(5))/120*Perimeter of Dodecahedron. To calculate Midsphere 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 Midsphere Radius of Dodecahedron?
In this formula, Midsphere Radius of Dodecahedron uses Perimeter of Dodecahedron. We can use 11 other way(s) to calculate the same, which is/are as follows -
  • Midsphere Radius of Dodecahedron = (3+sqrt(5))/4*Edge Length of Dodecahedron
  • Midsphere Radius of Dodecahedron = (3+sqrt(5))/4*((4*Volume of Dodecahedron)/(15+(7*sqrt(5))))^(1/3)
  • Midsphere Radius of Dodecahedron = (3+sqrt(5))/4*sqrt(Total Surface Area of Dodecahedron/(3*sqrt(25+(10*sqrt(5)))))
  • Midsphere Radius of Dodecahedron = (3+sqrt(5))/4*sqrt((4*Face Area of Dodecahedron)/sqrt(25+(10*sqrt(5))))
  • Midsphere Radius of Dodecahedron = (3+sqrt(5))/2*Face Diagonal of Dodecahedron/(1+sqrt(5))
  • Midsphere Radius of Dodecahedron = (3+sqrt(5))/20*Face Perimeter of Dodecahedron
  • Midsphere Radius of Dodecahedron = (3+sqrt(5))/2*Insphere Radius of Dodecahedron/sqrt((25+(11*sqrt(5)))/10)
  • Midsphere Radius of Dodecahedron = (3+sqrt(5))/2*Space Diagonal of Dodecahedron/(sqrt(3)*(1+sqrt(5)))
  • Midsphere Radius of Dodecahedron = (3+sqrt(5))*Circumsphere Radius of Dodecahedron/(sqrt(3)*(1+sqrt(5)))
  • Midsphere Radius of Dodecahedron = (3+sqrt(5))*(3*sqrt(25+(10*sqrt(5))))/(Surface to Volume Ratio of Dodecahedron*(15+(7*sqrt(5))))
  • Midsphere Radius of Dodecahedron = (3+sqrt(5))/4*sqrt((2*Lateral Surface Area of Dodecahedron)/(5*sqrt(25+(10*sqrt(5)))))
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