Surface to Volume Ratio of Icosahedron given Circumsphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5))))))
RA/V = (12*sqrt(3))/((3+sqrt(5))*((4*rc)/(sqrt(10+(2*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
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.
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.
STEP 1: Convert Input(s) to Base Unit
Circumsphere Radius of Icosahedron: 9 Meter --> 9 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
RA/V = (12*sqrt(3))/((3+sqrt(5))*((4*rc)/(sqrt(10+(2*sqrt(5)))))) --> (12*sqrt(3))/((3+sqrt(5))*((4*9)/(sqrt(10+(2*sqrt(5))))))
Evaluating ... ...
RA/V = 0.419469524121606
STEP 3: Convert Result to Output's Unit
0.419469524121606 1 per Meter --> No Conversion Required
FINAL ANSWER
0.419469524121606 0.41947 1 per Meter <-- Surface to Volume Ratio of Icosahedron
(Calculation completed in 00.004 seconds)

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Created by Dhruv Walia
Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
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11 Surface to Volume Ratio of Icosahedron Calculators

Surface to Volume Ratio of Icosahedron given Circumsphere Radius
​ Go Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5))))))
Surface to Volume Ratio of Icosahedron given Insphere Radius
​ Go Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))))
Surface to Volume Ratio of Icosahedron given Space Diagonal
​ Go Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*((2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5))))))
Surface to Volume Ratio of Icosahedron given Lateral Surface Area
​ Go Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3))))
Surface to Volume Ratio of Icosahedron given Total Surface Area
​ Go Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3))))
Surface to Volume Ratio of Icosahedron given Face Area
​ Go Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*sqrt((4*Face Area of Icosahedron)/sqrt(3)))
Surface to Volume Ratio of Icosahedron given Volume
​ Go Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*((12*Volume of Icosahedron)/(5*(3+sqrt(5))))^(1/3))
Surface to Volume Ratio of Icosahedron given Midsphere Radius
​ Go Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5))))
Surface to Volume Ratio of Icosahedron given Face Perimeter
​ Go Surface to Volume Ratio of Icosahedron = (36*sqrt(3))/((3+sqrt(5))*Face Perimeter of Icosahedron)
Surface to Volume Ratio of Icosahedron
​ Go Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*Edge Length of Icosahedron)
Surface to Volume Ratio of Icosahedron given Perimeter
​ Go Surface to Volume Ratio of Icosahedron = (360*sqrt(3))/((3+sqrt(5))*Perimeter of Icosahedron)

Surface to Volume Ratio of Icosahedron given Circumsphere Radius Formula

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

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 Surface to Volume Ratio of Icosahedron given Circumsphere Radius?

Surface to Volume Ratio of Icosahedron given Circumsphere Radius calculator uses Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))) to calculate the Surface to Volume Ratio of Icosahedron, The Surface to Volume Ratio of Icosahedron given Circumsphere Radius formula is defined as the numerical ratio of the total surface area to the volume of the Icosahedron and is calculated using the circumsphere radius of the Icosahedron. Surface to Volume Ratio of Icosahedron is denoted by RA/V symbol.

How to calculate Surface to Volume Ratio of Icosahedron given Circumsphere Radius using this online calculator? To use this online calculator for Surface to Volume Ratio of Icosahedron given Circumsphere Radius, enter Circumsphere Radius of Icosahedron (rc) and hit the calculate button. Here is how the Surface to Volume Ratio of Icosahedron given Circumsphere Radius calculation can be explained with given input values -> 0.41947 = (12*sqrt(3))/((3+sqrt(5))*((4*9)/(sqrt(10+(2*sqrt(5)))))).

FAQ

What is Surface to Volume Ratio of Icosahedron given Circumsphere Radius?
The Surface to Volume Ratio of Icosahedron given Circumsphere Radius formula is defined as the numerical ratio of the total surface area to the volume of the Icosahedron and is calculated using the circumsphere radius of the Icosahedron and is represented as RA/V = (12*sqrt(3))/((3+sqrt(5))*((4*rc)/(sqrt(10+(2*sqrt(5)))))) or Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))). 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.
How to calculate Surface to Volume Ratio of Icosahedron given Circumsphere Radius?
The Surface to Volume Ratio of Icosahedron given Circumsphere Radius formula is defined as the numerical ratio of the total surface area to the volume of the Icosahedron and is calculated using the circumsphere radius of the Icosahedron is calculated using Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5)))))). To calculate Surface to Volume Ratio of Icosahedron given Circumsphere Radius, you need Circumsphere Radius of Icosahedron (rc). With our tool, you need to enter the respective value for Circumsphere Radius 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 Surface to Volume Ratio of Icosahedron?
In this formula, Surface to Volume Ratio of Icosahedron uses Circumsphere Radius of Icosahedron. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*Edge Length of Icosahedron)
  • Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*((12*Insphere Radius of Icosahedron)/(sqrt(3)*(3+sqrt(5)))))
  • Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5))))
  • Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*((2*Space Diagonal of Icosahedron)/(sqrt(10+(2*sqrt(5))))))
  • Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3))))
  • Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*((12*Volume of Icosahedron)/(5*(3+sqrt(5))))^(1/3))
  • Surface to Volume Ratio of Icosahedron = (36*sqrt(3))/((3+sqrt(5))*Face Perimeter of Icosahedron)
  • Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*sqrt((4*Face Area of Icosahedron)/sqrt(3)))
  • Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3))))
  • Surface to Volume Ratio of Icosahedron = (360*sqrt(3))/((3+sqrt(5))*Perimeter of Icosahedron)
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