Circumsphere Radius of Icosahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)
rc = sqrt(10+(2*sqrt(5)))/4*(12*sqrt(3))/((3+sqrt(5))*RA/V)
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 Icosahedron - (Measured in Meter) - Circumsphere Radius of Icosahedron is the radius of the sphere that contains the Icosahedron in such a way that all the vertices are lying on the sphere.
Surface to Volume Ratio of Icosahedron - (Measured in 1 per Meter) - The Surface to Volume Ratio of Icosahedron is the numerical ratio of the total surface area to the volume of the Icosahedron.
STEP 1: Convert Input(s) to Base Unit
Surface to Volume Ratio of Icosahedron: 0.4 1 per Meter --> 0.4 1 per Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rc = sqrt(10+(2*sqrt(5)))/4*(12*sqrt(3))/((3+sqrt(5))*RA/V) --> sqrt(10+(2*sqrt(5)))/4*(12*sqrt(3))/((3+sqrt(5))*0.4)
Evaluating ... ...
rc = 9.43806429273614
STEP 3: Convert Result to Output's Unit
9.43806429273614 Meter --> No Conversion Required
FINAL ANSWER
9.43806429273614 9.438064 Meter <-- Circumsphere Radius of Icosahedron
(Calculation completed in 00.006 seconds)

Credits

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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
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11 Circumsphere Radius of Icosahedron Calculators

Circumsphere Radius of Icosahedron given Surface to Volume Ratio
Go Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)
Circumsphere Radius of Icosahedron given Lateral Surface Area
Go Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))
Circumsphere Radius of Icosahedron given Insphere Radius
Go Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))
Circumsphere Radius of Icosahedron given Total Surface Area
Go Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))
Circumsphere Radius of Icosahedron given Face Area
Go Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*sqrt((4*Face Area of Icosahedron)/sqrt(3))
Circumsphere Radius of Icosahedron given Volume
Go Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*((12*Volume of Icosahedron)/(5*(3+sqrt(5))))^(1/3)
Circumsphere Radius of Icosahedron given Midsphere Radius
Go Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(4*Midsphere Radius of Icosahedron)/(1+sqrt(5))
Circumsphere Radius of Icosahedron given Face Perimeter
Go Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))*Face Perimeter of Icosahedron/12
Circumsphere Radius of Icosahedron given Perimeter
Go Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))*Perimeter of Icosahedron/120
Circumsphere Radius of Icosahedron
Go Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*Edge Length of Icosahedron
Circumsphere Radius of Icosahedron given Space Diagonal
Go Circumsphere Radius of Icosahedron = Space Diagonal of Icosahedron/2

Circumsphere Radius of Icosahedron given Surface to Volume Ratio Formula

Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)
rc = sqrt(10+(2*sqrt(5)))/4*(12*sqrt(3))/((3+sqrt(5))*RA/V)

What is an Icosahedron?

An Icosahedron is a symmetric and closed three dimensional shape with 20 identical equilateral triangular faces. It is a Platonic solid, which has 20 faces, 12 vertices and 30 edges. At each vertex, five equilateral triangular faces meet and at each edge, two equilateral triangular faces meet.

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 Icosahedron given Surface to Volume Ratio?

Circumsphere Radius of Icosahedron given Surface to Volume Ratio calculator uses Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron) to calculate the Circumsphere Radius of Icosahedron, The Circumsphere Radius of Icosahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that contains the Icosahedron in such a way that all the vertices are lying on the sphere and is calculated using the surface to volume ratio of the Icosahedron. Circumsphere Radius of Icosahedron is denoted by rc symbol.

How to calculate Circumsphere Radius of Icosahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Circumsphere Radius of Icosahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Icosahedron (RA/V) and hit the calculate button. Here is how the Circumsphere Radius of Icosahedron given Surface to Volume Ratio calculation can be explained with given input values -> 9.438064 = sqrt(10+(2*sqrt(5)))/4*(12*sqrt(3))/((3+sqrt(5))*0.4).

FAQ

What is Circumsphere Radius of Icosahedron given Surface to Volume Ratio?
The Circumsphere Radius of Icosahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that contains the Icosahedron in such a way that all the vertices are lying on the sphere and is calculated using the surface to volume ratio of the Icosahedron and is represented as rc = sqrt(10+(2*sqrt(5)))/4*(12*sqrt(3))/((3+sqrt(5))*RA/V) or Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron). The Surface to Volume Ratio of Icosahedron is the numerical ratio of the total surface area to the volume of the Icosahedron.
How to calculate Circumsphere Radius of Icosahedron given Surface to Volume Ratio?
The Circumsphere Radius of Icosahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that contains the Icosahedron in such a way that all the vertices are lying on the sphere and is calculated using the surface to volume ratio of the Icosahedron is calculated using Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron). To calculate Circumsphere Radius of Icosahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Icosahedron (RA/V). With our tool, you need to enter the respective value for Surface to Volume Ratio of Icosahedron 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 Icosahedron?
In this formula, Circumsphere Radius of Icosahedron uses Surface to Volume Ratio of Icosahedron. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*Edge Length of Icosahedron
  • Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))
  • Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*(4*Midsphere Radius of Icosahedron)/(1+sqrt(5))
  • Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*((12*Volume of Icosahedron)/(5*(3+sqrt(5))))^(1/3)
  • Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))
  • Circumsphere Radius of Icosahedron = Space Diagonal of Icosahedron/2
  • Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))*Face Perimeter of Icosahedron/12
  • Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*sqrt((4*Face Area of Icosahedron)/sqrt(3))
  • Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))/4*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))
  • Circumsphere Radius of Icosahedron = sqrt(10+(2*sqrt(5)))*Perimeter of Icosahedron/120
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