Insphere Radius of Triakis Icosahedron given Surface to Volume Ratio Calculator

✖Surface to Volume Ratio of Triakis Icosahedron is what part of or fraction of total volume of Triakis Icosahedron is the total surface area.ⓘ Surface to Volume Ratio of Triakis Icosahedron [R_A/V]

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

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Formula

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Insphere Radius of Triakis Icosahedron given Surface to Volume Ratio

Formula

`"r"_{"i"} = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*((12*(sqrt(109-(30*sqrt(5)))))/((5+(7*sqrt(5)))*"R"_{"A/V"}))`

Example

`"6m"=((sqrt((10*(33+(13*sqrt(5))))/61))/4)*((12*(sqrt(109-(30*sqrt(5)))))/((5+(7*sqrt(5)))*"0.5m⁻¹"))`

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Insphere Radius of Triakis Icosahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Insphere Radius of Triakis Icosahedron = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*((12*(sqrt(109-(30*sqrt(5)))))/((5+(7*sqrt(5)))*Surface to Volume Ratio of Triakis Icosahedron))
r_i = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*((12*(sqrt(109-(30*sqrt(5)))))/((5+(7*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 Triakis Icosahedron - (Measured in Meter) - Insphere Radius of Triakis Icosahedron is the radius of the sphere that is contained by the Triakis Icosahedron in such a way that all the faces just touching the sphere.
Surface to Volume Ratio of Triakis Icosahedron - (Measured in 1 per Meter) - Surface to Volume Ratio of Triakis Icosahedron is what part of or fraction of total volume of Triakis Icosahedron is the total surface area.

STEP 1: Convert Input(s) to Base Unit

Surface to Volume Ratio of Triakis Icosahedron: 0.5 1 per Meter --> 0.5 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*((12*(sqrt(109-(30*sqrt(5)))))/((5+(7*sqrt(5)))*R_A/V)) --> ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*((12*(sqrt(109-(30*sqrt(5)))))/((5+(7*sqrt(5)))*0.5))

Evaluating ... ...

r_i = 6

STEP 3: Convert Result to Output's Unit

6 Meter --> No Conversion Required

FINAL ANSWER

6 Meter <-- Insphere Radius of Triakis Icosahedron

(Calculation completed in 00.004 seconds)

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< 6 Insphere Radius of Triakis Icosahedron Calculators

Insphere Radius of Triakis Icosahedron given Surface to Volume Ratio

Go Insphere Radius of Triakis Icosahedron = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*((12*(sqrt(109-(30*sqrt(5)))))/((5+(7*sqrt(5)))*Surface to Volume Ratio of Triakis Icosahedron))

Insphere Radius of Triakis Icosahedron given Total Surface Area

Go Insphere Radius of Triakis Icosahedron = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*(sqrt((11*Total Surface Area of Triakis Icosahedron)/(15*(sqrt(109-(30*sqrt(5)))))))

Insphere Radius of Triakis Icosahedron given Pyramidal Edge Length

Go Insphere Radius of Triakis Icosahedron = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*((22*Pyramidal Edge Length of Triakis Icosahedron)/(15-sqrt(5)))

Insphere Radius of Triakis Icosahedron given Volume

Go Insphere Radius of Triakis Icosahedron = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*(((44*Volume of Triakis Icosahedron)/(5*(5+(7*sqrt(5)))))^(1/3))

Insphere Radius of Triakis Icosahedron given Midsphere Radius

Go Insphere Radius of Triakis Icosahedron = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*((4*Midsphere Radius of Triakis Icosahedron)/(1+sqrt(5)))

Insphere Radius of Triakis Icosahedron

Go Insphere Radius of Triakis Icosahedron = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*Icosahedral Edge Length of Triakis Icosahedron

Insphere Radius of Triakis Icosahedron given Surface to Volume Ratio Formula

What is Triakis Icosahedron?

The Triakis Icosahedron is a three-dimensional polyhedron created from the dual of the truncated dodecahedron. Because of this, it shares the same full icosahedral symmetry group as the dodecahedron and the truncated dodecahedron. It can also be constructed by adding short triangular pyramids onto the faces of an icosahedron. It has 60 faces, 90 edges, 32 vertices.

How to Calculate Insphere Radius of Triakis Icosahedron given Surface to Volume Ratio?

Insphere Radius of Triakis Icosahedron given Surface to Volume Ratio calculator uses Insphere Radius of Triakis Icosahedron = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*((12*(sqrt(109-(30*sqrt(5)))))/((5+(7*sqrt(5)))*Surface to Volume Ratio of Triakis Icosahedron)) to calculate the Insphere Radius of Triakis Icosahedron, Insphere Radius of Triakis Icosahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that is contained by the Triakis Icosahedron in such a way that all the faces just touching the sphere, calculated using surface to volume ratio of Triakis Icosahedron. Insphere Radius of Triakis Icosahedron is denoted by r_i symbol.

How to calculate Insphere Radius of Triakis Icosahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Insphere Radius of Triakis Icosahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Triakis Icosahedron (R_A/V) and hit the calculate button. Here is how the Insphere Radius of Triakis Icosahedron given Surface to Volume Ratio calculation can be explained with given input values -> 6 = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*((12*(sqrt(109-(30*sqrt(5)))))/((5+(7*sqrt(5)))*0.5)).

FAQ

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

Insphere Radius of Triakis Icosahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that is contained by the Triakis Icosahedron in such a way that all the faces just touching the sphere, calculated using surface to volume ratio of Triakis Icosahedron and is represented as r_i = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*((12*(sqrt(109-(30*sqrt(5)))))/((5+(7*sqrt(5)))*R_A/V)) or Insphere Radius of Triakis Icosahedron = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*((12*(sqrt(109-(30*sqrt(5)))))/((5+(7*sqrt(5)))*Surface to Volume Ratio of Triakis Icosahedron)). Surface to Volume Ratio of Triakis Icosahedron is what part of or fraction of total volume of Triakis Icosahedron is the total surface area.

How to calculate Insphere Radius of Triakis Icosahedron given Surface to Volume Ratio?

Insphere Radius of Triakis Icosahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that is contained by the Triakis Icosahedron in such a way that all the faces just touching the sphere, calculated using surface to volume ratio of Triakis Icosahedron is calculated using Insphere Radius of Triakis Icosahedron = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*((12*(sqrt(109-(30*sqrt(5)))))/((5+(7*sqrt(5)))*Surface to Volume Ratio of Triakis Icosahedron)). To calculate Insphere Radius of Triakis Icosahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Triakis Icosahedron (R_A/V). With our tool, you need to enter the respective value for Surface to Volume Ratio of Triakis 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 Triakis Icosahedron?

In this formula, Insphere Radius of Triakis Icosahedron uses Surface to Volume Ratio of Triakis Icosahedron. We can use 5 other way(s) to calculate the same, which is/are as follows -

Insphere Radius of Triakis Icosahedron = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*Icosahedral Edge Length of Triakis Icosahedron
Insphere Radius of Triakis Icosahedron = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*((22*Pyramidal Edge Length of Triakis Icosahedron)/(15-sqrt(5)))
Insphere Radius of Triakis Icosahedron = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*(sqrt((11*Total Surface Area of Triakis Icosahedron)/(15*(sqrt(109-(30*sqrt(5)))))))
Insphere Radius of Triakis Icosahedron = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*(((44*Volume of Triakis Icosahedron)/(5*(5+(7*sqrt(5)))))^(1/3))
Insphere Radius of Triakis Icosahedron = ((sqrt((10*(33+(13*sqrt(5))))/61))/4)*((4*Midsphere Radius of Triakis Icosahedron)/(1+sqrt(5)))

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