Surface to Volume Ratio of Triakis Icosahedron given Insphere Radius Calculator

✖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 [r_i]

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✖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 given Insphere Radius [R_A/V]

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Surface to Volume Ratio of Triakis Icosahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

STEP 1: Convert Input(s) to Base Unit

Insphere Radius of Triakis Icosahedron: 6 Meter --> 6 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_A/V = ((12*(sqrt(109-(30*sqrt(5)))))/(5+(7*sqrt(5))))*((sqrt((10*(33+(13*sqrt(5))))/61))/(4*r_i)) --> ((12*(sqrt(109-(30*sqrt(5)))))/(5+(7*sqrt(5))))*((sqrt((10*(33+(13*sqrt(5))))/61))/(4*6))

Evaluating ... ...

R_A/V = 0.5

STEP 3: Convert Result to Output's Unit

0.5 1 per Meter --> No Conversion Required

FINAL ANSWER

0.5 1 per Meter <-- Surface to Volume Ratio of Triakis Icosahedron

(Calculation completed in 00.007 seconds)

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Walchand College of Engineering (WCE), Sangli

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< Surface to Volume Ratio of Triakis Icosahedron Calculators

Surface to Volume Ratio of Triakis Icosahedron given Total Surface Area

LaTeX Go Surface to Volume Ratio of Triakis Icosahedron = ((12*(sqrt(109-(30*sqrt(5)))))/(5+(7*sqrt(5))))*(sqrt((15*(sqrt(109-(30*sqrt(5)))))/(11*Total Surface Area of Triakis Icosahedron)))

Surface to Volume Ratio of Triakis Icosahedron given Pyramidal Edge Length

LaTeX Go Surface to Volume Ratio of Triakis Icosahedron = ((12*(sqrt(109-(30*sqrt(5)))))/(5+(7*sqrt(5))))*((15-sqrt(5))/(22*Pyramidal Edge Length of Triakis Icosahedron))

Surface to Volume Ratio of Triakis Icosahedron given Volume

LaTeX Go Surface to Volume Ratio of Triakis Icosahedron = ((12*(sqrt(109-(30*sqrt(5)))))/(5+(7*sqrt(5))))*(((5*(5+(7*sqrt(5))))/(44*Volume of Triakis Icosahedron))^(1/3))

Surface to Volume Ratio of Triakis Icosahedron

LaTeX Go Surface to Volume Ratio of Triakis Icosahedron = ((12*(sqrt(109-(30*sqrt(5)))))/((5+(7*sqrt(5)))*Icosahedral Edge Length of Triakis Icosahedron))

Surface to Volume Ratio of Triakis Icosahedron given Insphere Radius Formula

LaTeX Go

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 Surface to Volume Ratio of Triakis Icosahedron given Insphere Radius?

Surface to Volume Ratio of Triakis Icosahedron given Insphere Radius calculator uses Surface to Volume Ratio of Triakis Icosahedron = ((12*(sqrt(109-(30*sqrt(5)))))/(5+(7*sqrt(5))))*((sqrt((10*(33+(13*sqrt(5))))/61))/(4*Insphere Radius of Triakis Icosahedron)) to calculate the Surface to Volume Ratio of Triakis Icosahedron, Surface to Volume Ratio of Triakis Icosahedron given Insphere Radius formula is defined as what part or what fraction of total volume of Triakis Icosahedron is the total surface area, calculated using insphere radius of Triakis Icosahedron. Surface to Volume Ratio of Triakis Icosahedron is denoted by R_A/V symbol.

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

FAQ

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

Surface to Volume Ratio of Triakis Icosahedron given Insphere Radius formula is defined as what part or what fraction of total volume of Triakis Icosahedron is the total surface area, calculated using insphere radius of Triakis Icosahedron and is represented as R_A/V = ((12*(sqrt(109-(30*sqrt(5)))))/(5+(7*sqrt(5))))*((sqrt((10*(33+(13*sqrt(5))))/61))/(4*r_i)) or Surface to Volume Ratio of Triakis Icosahedron = ((12*(sqrt(109-(30*sqrt(5)))))/(5+(7*sqrt(5))))*((sqrt((10*(33+(13*sqrt(5))))/61))/(4*Insphere Radius of Triakis Icosahedron)). 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.

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

Surface to Volume Ratio of Triakis Icosahedron given Insphere Radius formula is defined as what part or what fraction of total volume of Triakis Icosahedron is the total surface area, calculated using insphere radius of Triakis Icosahedron is calculated using Surface to Volume Ratio of Triakis Icosahedron = ((12*(sqrt(109-(30*sqrt(5)))))/(5+(7*sqrt(5))))*((sqrt((10*(33+(13*sqrt(5))))/61))/(4*Insphere Radius of Triakis Icosahedron)). To calculate Surface to Volume Ratio of Triakis Icosahedron given Insphere Radius, you need Insphere Radius of Triakis Icosahedron (r_i). With our tool, you need to enter the respective value for Insphere Radius 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 Surface to Volume Ratio of Triakis Icosahedron?

In this formula, Surface to Volume Ratio of Triakis Icosahedron uses Insphere Radius of Triakis Icosahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Surface to Volume Ratio of Triakis Icosahedron = ((12*(sqrt(109-(30*sqrt(5)))))/((5+(7*sqrt(5)))*Icosahedral Edge Length of Triakis Icosahedron))
Surface to Volume Ratio of Triakis Icosahedron = ((12*(sqrt(109-(30*sqrt(5)))))/(5+(7*sqrt(5))))*((15-sqrt(5))/(22*Pyramidal Edge Length of Triakis Icosahedron))
Surface to Volume Ratio of Triakis Icosahedron = ((12*(sqrt(109-(30*sqrt(5)))))/(5+(7*sqrt(5))))*(sqrt((15*(sqrt(109-(30*sqrt(5)))))/(11*Total Surface Area of Triakis Icosahedron)))

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