Surface to Volume Ratio of Icosahedron Solution

STEP 0: Pre-Calculation Summary
Formula Used
Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*Edge Length of Icosahedron)
RA/V = (12*sqrt(3))/((3+sqrt(5))*le)
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - Square root function, 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.
Edge Length of Icosahedron - (Measured in Meter) - Edge Length of Icosahedron is the length of any of edges of the Icosahedron or the distance between any pair of adjacent vertices of the Icosahedron.
STEP 1: Convert Input(s) to Base Unit
Edge Length of Icosahedron: 10 Meter --> 10 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
RA/V = (12*sqrt(3))/((3+sqrt(5))*le) --> (12*sqrt(3))/((3+sqrt(5))*10)
Evaluating ... ...
RA/V = 0.396950722949765
STEP 3: Convert Result to Output's Unit
0.396950722949765 1 per Meter --> No Conversion Required
FINAL ANSWER
0.396950722949765 0.396951 1 per Meter <-- Surface to Volume Ratio of Icosahedron
(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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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 Formula

Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*Edge Length of Icosahedron)
RA/V = (12*sqrt(3))/((3+sqrt(5))*le)

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?

Surface to Volume Ratio of Icosahedron calculator uses Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*Edge Length of Icosahedron) to calculate the Surface to Volume Ratio of Icosahedron, The Surface to Volume Ratio of Icosahedron formula is defined as the numerical ratio of the total surface area to the volume of the Icosahedron. Surface to Volume Ratio of Icosahedron is denoted by RA/V symbol.

How to calculate Surface to Volume Ratio of Icosahedron using this online calculator? To use this online calculator for Surface to Volume Ratio of Icosahedron, enter Edge Length of Icosahedron (le) and hit the calculate button. Here is how the Surface to Volume Ratio of Icosahedron calculation can be explained with given input values -> 0.396951 = (12*sqrt(3))/((3+sqrt(5))*10).

FAQ

What is Surface to Volume Ratio of Icosahedron?
The Surface to Volume Ratio of Icosahedron formula is defined as the numerical ratio of the total surface area to the volume of the Icosahedron and is represented as RA/V = (12*sqrt(3))/((3+sqrt(5))*le) or Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*Edge Length of Icosahedron). Edge Length of Icosahedron is the length of any of edges of the Icosahedron or the distance between any pair of adjacent vertices of the Icosahedron.
How to calculate Surface to Volume Ratio of Icosahedron?
The Surface to Volume Ratio of Icosahedron formula is defined as the numerical ratio of the total surface area to the volume of the Icosahedron is calculated using Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*Edge Length of Icosahedron). To calculate Surface to Volume Ratio of Icosahedron, you need Edge Length of Icosahedron (le). With our tool, you need to enter the respective value for Edge Length 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 Edge Length 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))*((4*Circumsphere Radius of Icosahedron)/(sqrt(10+(2*sqrt(5))))))
  • 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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