Circumsphere Radius of Dodecahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
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))))
rc = sqrt(3)*(1+sqrt(5))*(3*sqrt(25+(10*sqrt(5))))/(RA/V*(15+(7*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
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.
Surface to Volume Ratio of Dodecahedron - (Measured in 1 per Meter) - The Surface to Volume Ratio of Dodecahedron is the numerical ratio of the total surface area to the volume of the Dodecahedron.
STEP 1: Convert Input(s) to Base Unit
Surface to Volume Ratio of Dodecahedron: 0.3 1 per Meter --> 0.3 1 per Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rc = sqrt(3)*(1+sqrt(5))*(3*sqrt(25+(10*sqrt(5))))/(RA/V*(15+(7*sqrt(5)))) --> sqrt(3)*(1+sqrt(5))*(3*sqrt(25+(10*sqrt(5))))/(0.3*(15+(7*sqrt(5))))
Evaluating ... ...
rc = 12.5840857236482
STEP 3: Convert Result to Output's Unit
12.5840857236482 Meter --> No Conversion Required
FINAL ANSWER
12.5840857236482 12.58409 Meter <-- Circumsphere Radius of Dodecahedron
(Calculation completed in 00.004 seconds)

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Circumsphere Radius of Dodecahedron Calculators

Circumsphere Radius of Dodecahedron given Total Surface Area
​ LaTeX ​ 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 Volume
​ LaTeX ​ 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
​ LaTeX ​ Go Circumsphere Radius of Dodecahedron = sqrt(3)*(1+sqrt(5))*Edge Length of Dodecahedron/4
Circumsphere Radius of Dodecahedron given Face Diagonal
​ LaTeX ​ Go Circumsphere Radius of Dodecahedron = sqrt(3)/2*Face Diagonal of Dodecahedron

Circumsphere Radius of Dodecahedron given Surface to Volume Ratio Formula

​LaTeX ​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))))
rc = sqrt(3)*(1+sqrt(5))*(3*sqrt(25+(10*sqrt(5))))/(RA/V*(15+(7*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 Circumsphere Radius of Dodecahedron given Surface to Volume Ratio?

Circumsphere Radius of Dodecahedron given Surface to Volume Ratio calculator uses 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)))) to calculate the Circumsphere Radius of Dodecahedron, The Circumsphere Radius of Dodecahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that contains the Dodecahedron in such a way that all the vertices are lying on the sphere, and calculated using surface to volume ratio of Dodecahedron. Circumsphere Radius of Dodecahedron is denoted by rc symbol.

How to calculate Circumsphere Radius of Dodecahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Circumsphere Radius of Dodecahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Dodecahedron (RA/V) and hit the calculate button. Here is how the Circumsphere Radius of Dodecahedron given Surface to Volume Ratio calculation can be explained with given input values -> 12.58409 = sqrt(3)*(1+sqrt(5))*(3*sqrt(25+(10*sqrt(5))))/(0.3*(15+(7*sqrt(5)))).

FAQ

What is Circumsphere Radius of Dodecahedron given Surface to Volume Ratio?
The Circumsphere Radius of Dodecahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that contains the Dodecahedron in such a way that all the vertices are lying on the sphere, and calculated using surface to volume ratio of Dodecahedron and is represented as rc = sqrt(3)*(1+sqrt(5))*(3*sqrt(25+(10*sqrt(5))))/(RA/V*(15+(7*sqrt(5)))) or 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)))). The Surface to Volume Ratio of Dodecahedron is the numerical ratio of the total surface area to the volume of the Dodecahedron.
How to calculate Circumsphere Radius of Dodecahedron given Surface to Volume Ratio?
The Circumsphere Radius of Dodecahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that contains the Dodecahedron in such a way that all the vertices are lying on the sphere, and calculated using surface to volume ratio of Dodecahedron is calculated using 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)))). To calculate Circumsphere Radius of Dodecahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Dodecahedron (RA/V). With our tool, you need to enter the respective value for Surface to Volume Ratio 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 Surface to Volume Ratio of Dodecahedron. We can use 3 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
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