Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio Calculator

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

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

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Formula

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Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio

Formula

`"r"_{"i"} = ((sqrt((402+(195*sqrt(2)))/194))/2)*((12*sqrt(543+(176*sqrt(2))))/("R"_{"A/V"}*(sqrt(6*(986+(607*sqrt(2)))))))`

Example

`"15m"=((sqrt((402+(195*sqrt(2)))/194))/2)*((12*sqrt(543+(176*sqrt(2))))/("0.2m⁻¹"*(sqrt(6*(986+(607*sqrt(2)))))))`

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Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*((12*sqrt(543+(176*sqrt(2))))/(Surface to Volume Ratio of Hexakis Octahedron*(sqrt(6*(986+(607*sqrt(2)))))))
r_i = ((sqrt((402+(195*sqrt(2)))/194))/2)*((12*sqrt(543+(176*sqrt(2))))/(R_A/V*(sqrt(6*(986+(607*sqrt(2)))))))
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 Hexakis Octahedron - (Measured in Meter) - Insphere Radius of Hexakis Octahedron is defined as the radius of the sphere that is contained by the Hexakis Octahedron in such a way that all the faces just touching the sphere.
Surface to Volume Ratio of Hexakis Octahedron - (Measured in 1 per Meter) - Surface to Volume Ratio of Hexakis Octahedron is what part of or fraction of total volume of Hexakis Octahedron is the total surface area.

STEP 1: Convert Input(s) to Base Unit

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = ((sqrt((402+(195*sqrt(2)))/194))/2)*((12*sqrt(543+(176*sqrt(2))))/(R_A/V*(sqrt(6*(986+(607*sqrt(2))))))) --> ((sqrt((402+(195*sqrt(2)))/194))/2)*((12*sqrt(543+(176*sqrt(2))))/(0.2*(sqrt(6*(986+(607*sqrt(2)))))))

Evaluating ... ...

r_i = 15

STEP 3: Convert Result to Output's Unit

15 Meter --> No Conversion Required

FINAL ANSWER

15 Meter <-- Insphere Radius of Hexakis Octahedron

(Calculation completed in 00.020 seconds)

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< 8 Insphere Radius of Hexakis Octahedron Calculators

Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio

Go Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*((12*sqrt(543+(176*sqrt(2))))/(Surface to Volume Ratio of Hexakis Octahedron*(sqrt(6*(986+(607*sqrt(2)))))))

Insphere Radius of Hexakis Octahedron given Total Surface Area

Go Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*(sqrt((7*Total Surface Area of Hexakis Octahedron)/(3*sqrt(543+(176*sqrt(2))))))

Insphere Radius of Hexakis Octahedron given Truncated Cuboctahedron Edge

Go Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*(2/7)*(sqrt(60+(6*sqrt(2))))*(Truncated Cuboctahedron Edge of Hexakis Octahedron)

Insphere Radius of Hexakis Octahedron given Volume

Go Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*(((28*Volume of Hexakis Octahedron)/(sqrt(6*(986+(607*sqrt(2))))))^(1/3))

Insphere Radius of Hexakis Octahedron given Midsphere Radius

Go Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*((4*Midsphere Radius of Hexakis Octahedron)/(1+(2*sqrt(2))))

Insphere Radius of Hexakis Octahedron given Medium Edge

Go Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*((14*Medium Edge of Hexakis Octahedron)/(3*(1+(2*sqrt(2)))))

Insphere Radius of Hexakis Octahedron given Short Edge

Go Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*((14*Short Edge of Hexakis Octahedron)/(10-sqrt(2)))

Insphere Radius of Hexakis Octahedron

Go Insphere Radius of Hexakis Octahedron = (Long Edge of Hexakis Octahedron/2)*(sqrt((402+(195*sqrt(2)))/194))

Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio Formula

What is Hexakis Octahedron?

In geometry, a Hexakis Octahedron (also called hexoctahedron, disdyakis dodecahedron, octakis cube, octakis hexahedron, kisrhombic dodecahedron), is a Catalan solid with 48 congruent triangular faces, 72 edges and 26 vertices. It is the dual of the Archimedean solid ‘truncated cuboctahedron’. As such it is face-transitive but with irregular face polygons.

How to Calculate Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio?

Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio calculator uses Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*((12*sqrt(543+(176*sqrt(2))))/(Surface to Volume Ratio of Hexakis Octahedron*(sqrt(6*(986+(607*sqrt(2))))))) to calculate the Insphere Radius of Hexakis Octahedron, Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that is contained by the Hexakis Octahedron in such a way that all the faces just touching the sphere, calculated using surface to volume ratio of Hexakis Octahedron. Insphere Radius of Hexakis Octahedron is denoted by r_i symbol.

How to calculate Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio using this online calculator? To use this online calculator for Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio, enter Surface to Volume Ratio of Hexakis Octahedron (R_A/V) and hit the calculate button. Here is how the Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio calculation can be explained with given input values -> 15 = ((sqrt((402+(195*sqrt(2)))/194))/2)*((12*sqrt(543+(176*sqrt(2))))/(0.2*(sqrt(6*(986+(607*sqrt(2))))))).

FAQ

What is Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio?

Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that is contained by the Hexakis Octahedron in such a way that all the faces just touching the sphere, calculated using surface to volume ratio of Hexakis Octahedron and is represented as r_i = ((sqrt((402+(195*sqrt(2)))/194))/2)*((12*sqrt(543+(176*sqrt(2))))/(R_A/V*(sqrt(6*(986+(607*sqrt(2))))))) or Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*((12*sqrt(543+(176*sqrt(2))))/(Surface to Volume Ratio of Hexakis Octahedron*(sqrt(6*(986+(607*sqrt(2))))))). Surface to Volume Ratio of Hexakis Octahedron is what part of or fraction of total volume of Hexakis Octahedron is the total surface area.

How to calculate Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio?

Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio formula is defined as the radius of the sphere that is contained by the Hexakis Octahedron in such a way that all the faces just touching the sphere, calculated using surface to volume ratio of Hexakis Octahedron is calculated using Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*((12*sqrt(543+(176*sqrt(2))))/(Surface to Volume Ratio of Hexakis Octahedron*(sqrt(6*(986+(607*sqrt(2))))))). To calculate Insphere Radius of Hexakis Octahedron given Surface to Volume Ratio, you need Surface to Volume Ratio of Hexakis Octahedron (R_A/V). With our tool, you need to enter the respective value for Surface to Volume Ratio of Hexakis Octahedron 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 Hexakis Octahedron?

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

Insphere Radius of Hexakis Octahedron = (Long Edge of Hexakis Octahedron/2)*(sqrt((402+(195*sqrt(2)))/194))
Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*((14*Medium Edge of Hexakis Octahedron)/(3*(1+(2*sqrt(2)))))
Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*((14*Short Edge of Hexakis Octahedron)/(10-sqrt(2)))
Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*(sqrt((7*Total Surface Area of Hexakis Octahedron)/(3*sqrt(543+(176*sqrt(2))))))
Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*(((28*Volume of Hexakis Octahedron)/(sqrt(6*(986+(607*sqrt(2))))))^(1/3))
Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*((4*Midsphere Radius of Hexakis Octahedron)/(1+(2*sqrt(2))))
Insphere Radius of Hexakis Octahedron = ((sqrt((402+(195*sqrt(2)))/194))/2)*(2/7)*(sqrt(60+(6*sqrt(2))))*(Truncated Cuboctahedron Edge of Hexakis Octahedron)

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