Midsphere Radius of Hexakis Icosahedron given Surface to Volume Ratio Calculator

✖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 [R_A/V]

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✖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 given Surface to Volume Ratio [r_m]

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Formula

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Midsphere Radius of Hexakis Icosahedron given Surface to Volume Ratio

Formula

`"r"_{"m"} = 1/8*(6/5*sqrt(10*(417+107*sqrt(5)))/("R"_{"A/V"}*sqrt(6*(185+82*sqrt(5)))))*(5+3*sqrt(5))`

Example

`"15.13139m"=1/8*(6/5*sqrt(10*(417+107*sqrt(5)))/("0.2m⁻¹"*sqrt(6*(185+82*sqrt(5)))))*(5+3*sqrt(5))`

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Midsphere Radius of Hexakis Icosahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Midsphere Radius of Hexakis Icosahedron = 1/8*(6/5*sqrt(10*(417+107*sqrt(5)))/(Surface to Volume Ratio of Hexakis Icosahedron*sqrt(6*(185+82*sqrt(5)))))*(5+3*sqrt(5))
r_m = 1/8*(6/5*sqrt(10*(417+107*sqrt(5)))/(R_A/V*sqrt(6*(185+82*sqrt(5)))))*(5+3*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

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.
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.

STEP 1: Convert Input(s) to Base Unit

Surface to Volume Ratio of Hexakis Icosahedron: 0.2 1 per Meter --> 0.2 1 per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_m = 1/8*(6/5*sqrt(10*(417+107*sqrt(5)))/(R_A/V*sqrt(6*(185+82*sqrt(5)))))*(5+3*sqrt(5)) --> 1/8*(6/5*sqrt(10*(417+107*sqrt(5)))/(0.2*sqrt(6*(185+82*sqrt(5)))))*(5+3*sqrt(5))

Evaluating ... ...

r_m = 15.1313905619247

STEP 3: Convert Result to Output's Unit

15.1313905619247 Meter --> No Conversion Required

FINAL ANSWER

15.1313905619247 ≈ 15.13139 Meter <-- Midsphere Radius of Hexakis Icosahedron

(Calculation completed in 00.004 seconds)

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< 8 Midsphere Radius of Hexakis Icosahedron Calculators

Midsphere Radius of Hexakis Icosahedron given Surface to Volume Ratio

Go Midsphere Radius of Hexakis Icosahedron = 1/8*(6/5*sqrt(10*(417+107*sqrt(5)))/(Surface to Volume Ratio of Hexakis Icosahedron*sqrt(6*(185+82*sqrt(5)))))*(5+3*sqrt(5))

Midsphere Radius of Hexakis Icosahedron given Total Surface Area

Go Midsphere Radius of Hexakis Icosahedron = 1/8*sqrt(44/15*Total Surface Area of Hexakis Icosahedron/sqrt(10*(417+107*sqrt(5))))*(5+3*sqrt(5))

Midsphere Radius of Hexakis Icosahedron given Insphere Radius

Go Midsphere Radius of Hexakis Icosahedron = 1/8*(4*Insphere Radius of Hexakis Icosahedron/sqrt(15/241*(275+119*sqrt(5))))*(5+3*sqrt(5))

Midsphere Radius of Hexakis Icosahedron given Truncated Icosidodecahedron Edge

Go Midsphere Radius of Hexakis Icosahedron = ((5+(3*sqrt(5)))/8)*(2/5)*(Truncated Edge of Hexakis Icosahedron)*(sqrt(15*(5-sqrt(5))))

Midsphere Radius of Hexakis Icosahedron given Volume

Go Midsphere Radius of Hexakis Icosahedron = 1/8*(88/25*Volume of Hexakis Icosahedron/sqrt(6*(185+82*sqrt(5))))^(1/3)*(5+3*sqrt(5))

Midsphere Radius of Hexakis Icosahedron given Medium Edge

Go Midsphere Radius of Hexakis Icosahedron = ((5+(3*sqrt(5)))/8)*((22*Medium Edge of Hexakis Icosahedron)/(3*(4+sqrt(5))))

Midsphere Radius of Hexakis Icosahedron given Short Edge

Go Midsphere Radius of Hexakis Icosahedron = ((5+(3*sqrt(5)))/8)*((44*Short Edge of Hexakis Icosahedron)/(5*(7-sqrt(5))))

Midsphere Radius of Hexakis Icosahedron

Go Midsphere Radius of Hexakis Icosahedron = Long Edge of Hexakis Icosahedron/8*(5+3*sqrt(5))

Midsphere Radius of Hexakis Icosahedron given Surface to Volume Ratio Formula

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 Midsphere Radius of Hexakis Icosahedron given Surface to Volume Ratio?

Midsphere Radius of Hexakis Icosahedron given Surface to Volume Ratio calculator uses Midsphere Radius of Hexakis Icosahedron = 1/8*(6/5*sqrt(10*(417+107*sqrt(5)))/(Surface to Volume Ratio of Hexakis Icosahedron*sqrt(6*(185+82*sqrt(5)))))*(5+3*sqrt(5)) to calculate the Midsphere Radius of Hexakis Icosahedron, The Midsphere Radius of Hexakis Icosahedron given Surface to Volume Ratio formula is defined as the radius of the sphere for which all the edges of the Hexakis Icosahedron become a tangent line on that sphere, calculated using the surface to volume ratio of Hexakis Icosahedron. Midsphere Radius of Hexakis Icosahedron is denoted by r_m symbol.

How to calculate Midsphere Radius of Hexakis Icosahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Midsphere Radius of Hexakis Icosahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Hexakis Icosahedron (R_A/V) and hit the calculate button. Here is how the Midsphere Radius of Hexakis Icosahedron given Surface to Volume Ratio calculation can be explained with given input values -> 15.13139 = 1/8*(6/5*sqrt(10*(417+107*sqrt(5)))/(0.2*sqrt(6*(185+82*sqrt(5)))))*(5+3*sqrt(5)).

FAQ

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

The Midsphere Radius of Hexakis Icosahedron given Surface to Volume Ratio formula is defined as the radius of the sphere for which all the edges of the Hexakis Icosahedron become a tangent line on that sphere, calculated using the surface to volume ratio of Hexakis Icosahedron and is represented as r_m = 1/8*(6/5*sqrt(10*(417+107*sqrt(5)))/(R_A/V*sqrt(6*(185+82*sqrt(5)))))*(5+3*sqrt(5)) or Midsphere Radius of Hexakis Icosahedron = 1/8*(6/5*sqrt(10*(417+107*sqrt(5)))/(Surface to Volume Ratio of Hexakis Icosahedron*sqrt(6*(185+82*sqrt(5)))))*(5+3*sqrt(5)). Surface to Volume Ratio of Hexakis Icosahedron is what part of or fraction of total volume of Hexakis Icosahedron is the total surface area.

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

The Midsphere Radius of Hexakis Icosahedron given Surface to Volume Ratio formula is defined as the radius of the sphere for which all the edges of the Hexakis Icosahedron become a tangent line on that sphere, calculated using the surface to volume ratio of Hexakis Icosahedron is calculated using Midsphere Radius of Hexakis Icosahedron = 1/8*(6/5*sqrt(10*(417+107*sqrt(5)))/(Surface to Volume Ratio of Hexakis Icosahedron*sqrt(6*(185+82*sqrt(5)))))*(5+3*sqrt(5)). To calculate Midsphere Radius of Hexakis Icosahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Hexakis Icosahedron (R_A/V). With our tool, you need to enter the respective value for Surface to Volume Ratio 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 Midsphere Radius of Hexakis Icosahedron?

In this formula, Midsphere Radius of Hexakis Icosahedron uses Surface to Volume Ratio of Hexakis Icosahedron. We can use 7 other way(s) to calculate the same, which is/are as follows -

Midsphere Radius of Hexakis Icosahedron = ((5+(3*sqrt(5)))/8)*((44*Short Edge of Hexakis Icosahedron)/(5*(7-sqrt(5))))
Midsphere Radius of Hexakis Icosahedron = ((5+(3*sqrt(5)))/8)*(2/5)*(Truncated Edge of Hexakis Icosahedron)*(sqrt(15*(5-sqrt(5))))
Midsphere Radius of Hexakis Icosahedron = ((5+(3*sqrt(5)))/8)*((22*Medium Edge of Hexakis Icosahedron)/(3*(4+sqrt(5))))
Midsphere Radius of Hexakis Icosahedron = Long Edge of Hexakis Icosahedron/8*(5+3*sqrt(5))
Midsphere Radius of Hexakis Icosahedron = 1/8*sqrt(44/15*Total Surface Area of Hexakis Icosahedron/sqrt(10*(417+107*sqrt(5))))*(5+3*sqrt(5))
Midsphere Radius of Hexakis Icosahedron = 1/8*(88/25*Volume of Hexakis Icosahedron/sqrt(6*(185+82*sqrt(5))))^(1/3)*(5+3*sqrt(5))
Midsphere Radius of Hexakis Icosahedron = 1/8*(4*Insphere Radius of Hexakis Icosahedron/sqrt(15/241*(275+119*sqrt(5))))*(5+3*sqrt(5))

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