Insphere Radius of Icosahedron given Surface to Volume Ratio Calculator

✖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 [R_A/V]

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✖Insphere Radius of Icosahedron is the radius of the sphere that is contained by the Icosahedron in such a way that all the faces just touching the sphere.ⓘ Insphere Radius of Icosahedron given Surface to Volume Ratio [r_i]

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Formula

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Insphere Radius of Icosahedron given Surface to Volume Ratio

Formula

`"r"_{"i"} = (sqrt(3)*(3+sqrt(5)))/12*(12*sqrt(3))/((3+sqrt(5))*"R"_{"A/V"})`

Example

`"7.5m"=(sqrt(3)*(3+sqrt(5)))/12*(12*sqrt(3))/((3+sqrt(5))*"0.4m⁻¹")`

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Insphere Radius of Icosahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*(12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)
r_i = (sqrt(3)*(3+sqrt(5)))/12*(12*sqrt(3))/((3+sqrt(5))*R_A/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

Insphere Radius of Icosahedron - (Measured in Meter) - Insphere Radius of Icosahedron is the radius of the sphere that is contained by the Icosahedron in such a way that all the faces just touching 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

r_i = (sqrt(3)*(3+sqrt(5)))/12*(12*sqrt(3))/((3+sqrt(5))*R_A/V) --> (sqrt(3)*(3+sqrt(5)))/12*(12*sqrt(3))/((3+sqrt(5))*0.4)

Evaluating ... ...

r_i = 7.5

STEP 3: Convert Result to Output's Unit

7.5 Meter --> No Conversion Required

FINAL ANSWER

7.5 Meter <-- Insphere Radius 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 Insphere Radius of Icosahedron Calculators

Insphere Radius of Icosahedron given Surface to Volume Ratio

Go Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*(12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)

Insphere Radius of Icosahedron given Circumsphere Radius

Go Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*(4*Circumsphere Radius of Icosahedron)/sqrt(10+(2*sqrt(5)))

Insphere Radius of Icosahedron given Lateral Surface Area

Go Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*sqrt((2*Lateral Surface Area of Icosahedron)/(9*sqrt(3)))

Insphere Radius of Icosahedron given Space Diagonal

Go Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*(2*Space Diagonal of Icosahedron)/sqrt(10+(2*sqrt(5)))

Insphere Radius of Icosahedron given Total Surface Area

Go Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*sqrt(Total Surface Area of Icosahedron/(5*sqrt(3)))

Insphere Radius of Icosahedron given Face Area

Go Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*sqrt((4*Face Area of Icosahedron)/sqrt(3))

Insphere Radius of Icosahedron given Volume

Go Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*((12*Volume of Icosahedron)/(5*(3+sqrt(5))))^(1/3)

Insphere Radius of Icosahedron given Midsphere Radius

Go Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*(4*Midsphere Radius of Icosahedron)/(1+sqrt(5))

Insphere Radius of Icosahedron given Face Perimeter

Go Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))*Face Perimeter of Icosahedron/36

Insphere Radius of Icosahedron

Go Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*Edge Length of Icosahedron

Insphere Radius of Icosahedron given Perimeter

Go Insphere Radius of Icosahedron = sqrt(3)*(3+sqrt(5))*Perimeter of Icosahedron/360

Insphere Radius of Icosahedron given Surface to Volume Ratio Formula

Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*(12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron)
r_i = (sqrt(3)*(3+sqrt(5)))/12*(12*sqrt(3))/((3+sqrt(5))*R_A/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 Insphere Radius of Icosahedron given Surface to Volume Ratio?

Insphere Radius of Icosahedron given Surface to Volume Ratio calculator uses Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*(12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron) to calculate the Insphere Radius of Icosahedron, The Insphere Radius of Icosahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that is contained by the Icosahedron in such a way that all the faces just touching the sphere, and calculated using the surface to volume ratio of the Icosahedron. Insphere Radius of Icosahedron is denoted by r_i symbol.

How to calculate Insphere Radius of Icosahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Insphere Radius of Icosahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Icosahedron (R_A/V) and hit the calculate button. Here is how the Insphere Radius of Icosahedron given Surface to Volume Ratio calculation can be explained with given input values -> 7.5 = (sqrt(3)*(3+sqrt(5)))/12*(12*sqrt(3))/((3+sqrt(5))*0.4).

FAQ

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

The Insphere Radius of Icosahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that is contained by the Icosahedron in such a way that all the faces just touching the sphere, and calculated using the surface to volume ratio of the Icosahedron and is represented as r_i = (sqrt(3)*(3+sqrt(5)))/12*(12*sqrt(3))/((3+sqrt(5))*R_A/V) or Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*(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 Insphere Radius of Icosahedron given Surface to Volume Ratio?

The Insphere Radius of Icosahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that is contained by the Icosahedron in such a way that all the faces just touching the sphere, and calculated using the surface to volume ratio of the Icosahedron is calculated using Insphere Radius of Icosahedron = (sqrt(3)*(3+sqrt(5)))/12*(12*sqrt(3))/((3+sqrt(5))*Surface to Volume Ratio of Icosahedron). To calculate Insphere Radius of Icosahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Icosahedron (R_A/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 Insphere Radius of Icosahedron?

In this formula, Insphere 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 -

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

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