Surface to Volume Ratio of Icosahedron given Midsphere Radius Calculator

✖The Midsphere Radius of Icosahedron is defined as radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere.ⓘ Midsphere Radius of Icosahedron [r_m]

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✖The Surface to Volume Ratio of Icosahedron is the numerical ratio of the total surface area to the volume of the Icosahedron.ⓘ Surface to Volume Ratio of Icosahedron given Midsphere Radius [R_A/V]

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Surface to Volume Ratio of Icosahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5))))
R_A/V = (12*sqrt(3))/((3+sqrt(5))*((4*r_m)/(1+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.
Midsphere Radius of Icosahedron - (Measured in Meter) - The Midsphere Radius of Icosahedron is defined as radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere.

STEP 1: Convert Input(s) to Base Unit

Midsphere Radius of Icosahedron: 8 Meter --> 8 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_A/V = (12*sqrt(3))/((3+sqrt(5))*((4*r_m)/(1+sqrt(5)))) --> (12*sqrt(3))/((3+sqrt(5))*((4*8)/(1+sqrt(5))))

Evaluating ... ...

R_A/V = 0.401424850994726

STEP 3: Convert Result to Output's Unit

0.401424850994726 1 per Meter --> No Conversion Required

FINAL ANSWER

0.401424850994726 ≈ 0.401425 1 per Meter <-- Surface to Volume Ratio of Icosahedron

(Calculation completed in 00.020 seconds)

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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

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< Surface to Volume Ratio of Icosahedron Calculators

Surface to Volume Ratio of Icosahedron given Circumsphere Radius

LaTeX 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

LaTeX 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 Midsphere Radius

LaTeX 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

LaTeX Go Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*Edge Length of Icosahedron)

Surface to Volume Ratio of Icosahedron given Midsphere Radius Formula

LaTeX Go

Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5))))
R_A/V = (12*sqrt(3))/((3+sqrt(5))*((4*r_m)/(1+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 Midsphere Radius?

Surface to Volume Ratio of Icosahedron given Midsphere Radius calculator uses Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5)))) to calculate the Surface to Volume Ratio of Icosahedron, The Surface to Volume Ratio of Icosahedron given Midsphere Radius formula is defined as the numerical ratio of the total surface area to the volume of the Icosahedron and is calculated using the midsphere radius of the Icosahedron. Surface to Volume Ratio of Icosahedron is denoted by R_A/V symbol.

How to calculate Surface to Volume Ratio of Icosahedron given Midsphere Radius using this online calculator? To use this online calculator for Surface to Volume Ratio of Icosahedron given Midsphere Radius, enter Midsphere Radius of Icosahedron (r_m) and hit the calculate button. Here is how the Surface to Volume Ratio of Icosahedron given Midsphere Radius calculation can be explained with given input values -> 0.401425 = (12*sqrt(3))/((3+sqrt(5))*((4*8)/(1+sqrt(5)))).

FAQ

What is Surface to Volume Ratio of Icosahedron given Midsphere Radius?

The Surface to Volume Ratio of Icosahedron given Midsphere Radius formula is defined as the numerical ratio of the total surface area to the volume of the Icosahedron and is calculated using the midsphere radius of the Icosahedron and is represented as R_A/V = (12*sqrt(3))/((3+sqrt(5))*((4*r_m)/(1+sqrt(5)))) or Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5)))). The Midsphere Radius of Icosahedron is defined as radius of the sphere for which all the edges of the Icosahedron become a tangent line on that sphere.

How to calculate Surface to Volume Ratio of Icosahedron given Midsphere Radius?

The Surface to Volume Ratio of Icosahedron given Midsphere Radius formula is defined as the numerical ratio of the total surface area to the volume of the Icosahedron and is calculated using the midsphere radius of the Icosahedron is calculated using Surface to Volume Ratio of Icosahedron = (12*sqrt(3))/((3+sqrt(5))*((4*Midsphere Radius of Icosahedron)/(1+sqrt(5)))). To calculate Surface to Volume Ratio of Icosahedron given Midsphere Radius, you need Midsphere Radius of Icosahedron (r_m). With our tool, you need to enter the respective value for Midsphere 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 Midsphere Radius of Icosahedron. We can use 3 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))*((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)))))

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