Circumsphere Radius of Dodecahedron given Perimeter Solution

STEP 0: Pre-Calculation Summary
Formula Used
Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))*Perimeter of Dodecahedron/120
rc = sqrt(3)*(1+sqrt(5))*P/120
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
Circumsphere Radius of Dodecahedron - (Measured in Meter) - Circumsphere Radius of Dodecahedron is the radius of the sphere that contains the Dodecahedron in such a way that all the vertices are lying on 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
rc = sqrt(3)*(1+sqrt(5))*P/120 --> sqrt(3)*(1+sqrt(5))*300/120
Evaluating ... ...
rc = 14.0125853844407
STEP 3: Convert Result to Output's Unit
14.0125853844407 Meter --> No Conversion Required
FINAL ANSWER
14.0125853844407 14.01259 Meter <-- Circumsphere Radius of Dodecahedron
(Calculation completed in 00.004 seconds)

Credits

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

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

Circumsphere Radius of Dodecahedron given Perimeter Formula

Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))*Perimeter of Dodecahedron/120
rc = sqrt(3)*(1+sqrt(5))*P/120

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 Circumsphere Radius of Dodecahedron given Perimeter?

Circumsphere Radius of Dodecahedron given Perimeter calculator uses Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))*Perimeter of Dodecahedron/120 to calculate the Circumsphere Radius of Dodecahedron, The Circumsphere Radius of Dodecahedron given Perimeter formula is defined as the radius of the sphere that contains the Dodecahedron in such a way that all the vertices of the Cube are touching the sphere, and calculated using the perimeter of the Dodecahedron. Circumsphere Radius of Dodecahedron is denoted by rc symbol.

How to calculate Circumsphere Radius of Dodecahedron given Perimeter using this online calculator? To use this online calculator for Circumsphere Radius of Dodecahedron given Perimeter, enter Perimeter of Dodecahedron (P) and hit the calculate button. Here is how the Circumsphere Radius of Dodecahedron given Perimeter calculation can be explained with given input values -> 14.01259 = sqrt(3)*(1+sqrt(5))*300/120.

FAQ

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