Surface to Volume Ratio of Hexakis Icosahedron given Midsphere Radius Calculator

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

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

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Surface to Volume Ratio of Hexakis Icosahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Surface to Volume Ratio of Hexakis Icosahedron = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((5+(3*sqrt(5)))/(8*Midsphere Radius of Hexakis Icosahedron))
R_A/V = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((5+(3*sqrt(5)))/(8*r_m))
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 Hexakis Icosahedron - (Measured in 1 per Meter) - Surface to Volume Ratio of Hexakis Icosahedron is what part of or fraction of total volume of Hexakis Icosahedron is the total surface area.
Midsphere Radius of Hexakis Icosahedron - (Measured in Meter) - Midsphere Radius of Hexakis Icosahedron is defined as the radius of the sphere for which all the edges of the Hexakis Icosahedron become a tangent line on that sphere.

STEP 1: Convert Input(s) to Base Unit

Midsphere Radius of Hexakis Icosahedron: 15 Meter --> 15 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_A/V = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((5+(3*sqrt(5)))/(8*r_m)) --> (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((5+(3*sqrt(5)))/(8*15))

Evaluating ... ...

R_A/V = 0.201751874158996

STEP 3: Convert Result to Output's Unit

0.201751874158996 1 per Meter --> No Conversion Required

FINAL ANSWER

0.201751874158996 ≈ 0.201752 1 per Meter <-- Surface to Volume Ratio of Hexakis Icosahedron

(Calculation completed in 00.020 seconds)

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Walchand College of Engineering (WCE), Sangli

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< Surface to Volume Ratio of Hexakis Icosahedron Calculators

Surface to Volume Ratio of Hexakis Icosahedron given Truncated Icosidodecahedron Edge

LaTeX Go Surface to Volume Ratio of Hexakis Icosahedron = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*(5/(2*Truncated Edge of Hexakis Icosahedron*(sqrt(15*(5-sqrt(5))))))

Surface to Volume Ratio of Hexakis Icosahedron given Medium Edge

LaTeX Go Surface to Volume Ratio of Hexakis Icosahedron = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((3*(4+sqrt(5)))/(22*Medium Edge of Hexakis Icosahedron))

Surface to Volume Ratio of Hexakis Icosahedron given Short Edge

LaTeX Go Surface to Volume Ratio of Hexakis Icosahedron = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((5*(7-sqrt(5)))/(44*Short Edge of Hexakis Icosahedron))

Surface to Volume Ratio of Hexakis Icosahedron

LaTeX Go Surface to Volume Ratio of Hexakis Icosahedron = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*(1/Long Edge of Hexakis Icosahedron)

Surface to Volume Ratio of Hexakis Icosahedron given Midsphere Radius Formula

LaTeX Go

What is Hexakis Icosahedron?

A Hexakis Icosahedron is a polyhedron with identical, but irregular triangle faces. It has thirty vertices with four edges, twenty vertices with six edges and twelve vertices with ten edges.
It has 120 faces, 180 edges, 62 vertices.

How to Calculate Surface to Volume Ratio of Hexakis Icosahedron given Midsphere Radius?

Surface to Volume Ratio of Hexakis Icosahedron given Midsphere Radius calculator uses Surface to Volume Ratio of Hexakis Icosahedron = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((5+(3*sqrt(5)))/(8*Midsphere Radius of Hexakis Icosahedron)) to calculate the Surface to Volume Ratio of Hexakis Icosahedron, Surface to Volume Ratio of Hexakis Icosahedron given Midsphere Radius formula is defined as what fraction of total volume of Hexakis Icosahedron is the total surface area of Hexakis Icosahedron, calculated using midsphere radius of Hexakis Icosahedron. Surface to Volume Ratio of Hexakis Icosahedron is denoted by R_A/V symbol.

How to calculate Surface to Volume Ratio of Hexakis Icosahedron given Midsphere Radius using this online calculator? To use this online calculator for Surface to Volume Ratio of Hexakis Icosahedron given Midsphere Radius, enter Midsphere Radius of Hexakis Icosahedron (r_m) and hit the calculate button. Here is how the Surface to Volume Ratio of Hexakis Icosahedron given Midsphere Radius calculation can be explained with given input values -> 0.201752 = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((5+(3*sqrt(5)))/(8*15)).

FAQ

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

Surface to Volume Ratio of Hexakis Icosahedron given Midsphere Radius formula is defined as what fraction of total volume of Hexakis Icosahedron is the total surface area of Hexakis Icosahedron, calculated using midsphere radius of Hexakis Icosahedron and is represented as R_A/V = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((5+(3*sqrt(5)))/(8*r_m)) or Surface to Volume Ratio of Hexakis Icosahedron = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((5+(3*sqrt(5)))/(8*Midsphere Radius of Hexakis Icosahedron)). Midsphere Radius of Hexakis Icosahedron is defined as the radius of the sphere for which all the edges of the Hexakis Icosahedron become a tangent line on that sphere.

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

Surface to Volume Ratio of Hexakis Icosahedron given Midsphere Radius formula is defined as what fraction of total volume of Hexakis Icosahedron is the total surface area of Hexakis Icosahedron, calculated using midsphere radius of Hexakis Icosahedron is calculated using Surface to Volume Ratio of Hexakis Icosahedron = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((5+(3*sqrt(5)))/(8*Midsphere Radius of Hexakis Icosahedron)). To calculate Surface to Volume Ratio of Hexakis Icosahedron given Midsphere Radius, you need Midsphere Radius of Hexakis Icosahedron (r_m). With our tool, you need to enter the respective value for Midsphere Radius of Hexakis 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 Hexakis Icosahedron?

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

Surface to Volume Ratio of Hexakis Icosahedron = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*(1/Long Edge of Hexakis Icosahedron)
Surface to Volume Ratio of Hexakis Icosahedron = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((3*(4+sqrt(5)))/(22*Medium Edge of Hexakis Icosahedron))
Surface to Volume Ratio of Hexakis Icosahedron = (6/5)*(sqrt((10*(417+(107*sqrt(5))))/(6*(185+(82*sqrt(5))))))*((5*(7-sqrt(5)))/(44*Short Edge of Hexakis Icosahedron))

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