Midsphere Radius of Tetrakis Hexahedron given Insphere Radius Calculator

✖Insphere Radius of Tetrakis Hexahedron is the radius of the sphere that is contained by the Tetrakis Hexahedron in such a way that all the faces just touching the sphere.ⓘ Insphere Radius of Tetrakis Hexahedron [r_i]

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✖Midsphere Radius of Tetrakis Hexahedron is the radius of the sphere for which all the edges of the Tetrakis Hexahedron become a tangent line on that sphere.ⓘ Midsphere Radius of Tetrakis Hexahedron given Insphere Radius [r_m]

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Formula

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Midsphere Radius of Tetrakis Hexahedron given Insphere Radius

Formula

`"r"_{"m"} = 1/sqrt(2)*((10*"r"_{"i"})/(3*sqrt(5)))`

Example

`"6.324555m"=1/sqrt(2)*((10*"6m")/(3*sqrt(5)))`

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Midsphere Radius of Tetrakis Hexahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Midsphere Radius of Tetrakis Hexahedron = 1/sqrt(2)*((10*Insphere Radius of Tetrakis Hexahedron)/(3*sqrt(5)))
r_m = 1/sqrt(2)*((10*r_i)/(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 Tetrakis Hexahedron - (Measured in Meter) - Midsphere Radius of Tetrakis Hexahedron is the radius of the sphere for which all the edges of the Tetrakis Hexahedron become a tangent line on that sphere.
Insphere Radius of Tetrakis Hexahedron - (Measured in Meter) - Insphere Radius of Tetrakis Hexahedron is the radius of the sphere that is contained by the Tetrakis Hexahedron in such a way that all the faces just touching the sphere.

STEP 1: Convert Input(s) to Base Unit

Insphere Radius of Tetrakis Hexahedron: 6 Meter --> 6 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_m = 1/sqrt(2)*((10*r_i)/(3*sqrt(5))) --> 1/sqrt(2)*((10*6)/(3*sqrt(5)))

Evaluating ... ...

r_m = 6.32455532033676

STEP 3: Convert Result to Output's Unit

6.32455532033676 Meter --> No Conversion Required

FINAL ANSWER

6.32455532033676 ≈ 6.324555 Meter <-- Midsphere Radius of Tetrakis Hexahedron

(Calculation completed in 00.004 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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Indian Institute of Information Technology (IIIT), Bhopal

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< 7 Midsphere Radius of Tetrakis Hexahedron Calculators

Midsphere Radius of Tetrakis Hexahedron given Total Surface Area

Go Midsphere Radius of Tetrakis Hexahedron = 1/sqrt(2)*sqrt(Total Surface Area of Tetrakis Hexahedron/(3*sqrt(5)))

Midsphere Radius of Tetrakis Hexahedron given Surface to Volume Ratio

Go Midsphere Radius of Tetrakis Hexahedron = 1/sqrt(2)*((2*sqrt(5))/(Surface to Volume Ratio of Tetrakis Hexahedron))

Midsphere Radius of Tetrakis Hexahedron given Insphere Radius

Go Midsphere Radius of Tetrakis Hexahedron = 1/sqrt(2)*((10*Insphere Radius of Tetrakis Hexahedron)/(3*sqrt(5)))

Midsphere Radius of Tetrakis Hexahedron given Pyramidal Edge Length

Go Midsphere Radius of Tetrakis Hexahedron = 4/3*(Pyramidal Edge Length of Tetrakis Hexahedron/sqrt(2))

Midsphere Radius of Tetrakis Hexahedron given Volume

Go Midsphere Radius of Tetrakis Hexahedron = 1/sqrt(2)*((2*Volume of Tetrakis Hexahedron)/3)^(1/3)

Midsphere Radius of Tetrakis Hexahedron

Go Midsphere Radius of Tetrakis Hexahedron = Cubical Edge Length of Tetrakis Hexahedron/sqrt(2)

Midsphere Radius of Tetrakis Hexahedron given Height

Go Midsphere Radius of Tetrakis Hexahedron = sqrt(2)/3*Height of Tetrakis Hexahedron

Midsphere Radius of Tetrakis Hexahedron given Insphere Radius Formula

Midsphere Radius of Tetrakis Hexahedron = 1/sqrt(2)*((10*Insphere Radius of Tetrakis Hexahedron)/(3*sqrt(5)))
r_m = 1/sqrt(2)*((10*r_i)/(3*sqrt(5)))

What is Tetrakis Hexahedron?

In geometry, a Tetrakis Hexahedron (also known as a tetrahexahedron, hextetrahedron, tetrakis cube, and kiscube) is a Catalan solid. Its dual is the truncated octahedron, an Archimedean solid. It can be called a disdyakis hexahedron or hexakis tetrahedron as the dual of an omnitruncated tetrahedron, and as the barycentric subdivision of a tetrahedron. It has 24 faces, 36 edges, 14 vertices.

How to Calculate Midsphere Radius of Tetrakis Hexahedron given Insphere Radius?

Midsphere Radius of Tetrakis Hexahedron given Insphere Radius calculator uses Midsphere Radius of Tetrakis Hexahedron = 1/sqrt(2)*((10*Insphere Radius of Tetrakis Hexahedron)/(3*sqrt(5))) to calculate the Midsphere Radius of Tetrakis Hexahedron, Midsphere Radius of Tetrakis Hexahedron given Insphere Radius formula is defined as the radius of the sphere for which all the edges of the Tetrakis Hexahedron become a tangent line on that sphere, calculated using insphere radius of Tetrakis Hexahedron. Midsphere Radius of Tetrakis Hexahedron is denoted by r_m symbol.

How to calculate Midsphere Radius of Tetrakis Hexahedron given Insphere Radius using this online calculator? To use this online calculator for Midsphere Radius of Tetrakis Hexahedron given Insphere Radius, enter Insphere Radius of Tetrakis Hexahedron (r_i) and hit the calculate button. Here is how the Midsphere Radius of Tetrakis Hexahedron given Insphere Radius calculation can be explained with given input values -> 6.324555 = 1/sqrt(2)*((10*6)/(3*sqrt(5))).

FAQ

What is Midsphere Radius of Tetrakis Hexahedron given Insphere Radius?

Midsphere Radius of Tetrakis Hexahedron given Insphere Radius formula is defined as the radius of the sphere for which all the edges of the Tetrakis Hexahedron become a tangent line on that sphere, calculated using insphere radius of Tetrakis Hexahedron and is represented as r_m = 1/sqrt(2)*((10*r_i)/(3*sqrt(5))) or Midsphere Radius of Tetrakis Hexahedron = 1/sqrt(2)*((10*Insphere Radius of Tetrakis Hexahedron)/(3*sqrt(5))). Insphere Radius of Tetrakis Hexahedron is the radius of the sphere that is contained by the Tetrakis Hexahedron in such a way that all the faces just touching the sphere.

How to calculate Midsphere Radius of Tetrakis Hexahedron given Insphere Radius?

Midsphere Radius of Tetrakis Hexahedron given Insphere Radius formula is defined as the radius of the sphere for which all the edges of the Tetrakis Hexahedron become a tangent line on that sphere, calculated using insphere radius of Tetrakis Hexahedron is calculated using Midsphere Radius of Tetrakis Hexahedron = 1/sqrt(2)*((10*Insphere Radius of Tetrakis Hexahedron)/(3*sqrt(5))). To calculate Midsphere Radius of Tetrakis Hexahedron given Insphere Radius, you need Insphere Radius of Tetrakis Hexahedron (r_i). With our tool, you need to enter the respective value for Insphere Radius of Tetrakis Hexahedron 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 Tetrakis Hexahedron?

In this formula, Midsphere Radius of Tetrakis Hexahedron uses Insphere Radius of Tetrakis Hexahedron. We can use 6 other way(s) to calculate the same, which is/are as follows -

Midsphere Radius of Tetrakis Hexahedron = Cubical Edge Length of Tetrakis Hexahedron/sqrt(2)
Midsphere Radius of Tetrakis Hexahedron = 1/sqrt(2)*((2*sqrt(5))/(Surface to Volume Ratio of Tetrakis Hexahedron))
Midsphere Radius of Tetrakis Hexahedron = 1/sqrt(2)*((2*Volume of Tetrakis Hexahedron)/3)^(1/3)
Midsphere Radius of Tetrakis Hexahedron = 1/sqrt(2)*sqrt(Total Surface Area of Tetrakis Hexahedron/(3*sqrt(5)))
Midsphere Radius of Tetrakis Hexahedron = sqrt(2)/3*Height of Tetrakis Hexahedron
Midsphere Radius of Tetrakis Hexahedron = 4/3*(Pyramidal Edge Length of Tetrakis Hexahedron/sqrt(2))

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