## Midsphere Radius of Octahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Midsphere Radius of Octahedron = sqrt(3/2)*Insphere Radius of Octahedron
rm = sqrt(3/2)*ri
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - Square root function, sqrt(Number)
Variables Used
Midsphere Radius of Octahedron - (Measured in Meter) - Midsphere Radius of Octahedron is the radius of the sphere for which all the edges of the Octahedron become a tangent line to that sphere.
Insphere Radius of Octahedron - (Measured in Meter) - Insphere Radius of Octahedron is the radius of the sphere that is contained by the Octahedron in such a way that all the faces are just touching the sphere.
STEP 1: Convert Input(s) to Base Unit
Insphere Radius of Octahedron: 4 Meter --> 4 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rm = sqrt(3/2)*ri --> sqrt(3/2)*4
Evaluating ... ...
rm = 4.89897948556636
STEP 3: Convert Result to Output's Unit
4.89897948556636 Meter --> No Conversion Required
4.89897948556636 4.898979 Meter <-- Midsphere Radius of Octahedron
(Calculation completed in 00.003 seconds)
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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
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## < 7 Midsphere Radius of Octahedron Calculators

Midsphere Radius of Octahedron given Total Surface Area
Midsphere Radius of Octahedron = sqrt(Total Surface Area of Octahedron/(2*sqrt(3)))/2
Midsphere Radius of Octahedron given Surface to Volume Ratio
Midsphere Radius of Octahedron = (3*sqrt(6))/(2*Surface to Volume Ratio of Octahedron)
Midsphere Radius of Octahedron given Volume
Midsphere Radius of Octahedron = ((3*Volume of Octahedron)/sqrt(2))^(1/3)/2
Midsphere Radius of Octahedron given Circumsphere Radius
Midsphere Radius of Octahedron = Circumsphere Radius of Octahedron/sqrt(2)
Midsphere Radius of Octahedron given Space Diagonal
Midsphere Radius of Octahedron = Space Diagonal of Octahedron/(2*sqrt(2))
Midsphere Radius of Octahedron given Insphere Radius
Midsphere Radius of Octahedron = sqrt(3/2)*Insphere Radius of Octahedron
Midsphere Radius of Octahedron
Midsphere Radius of Octahedron = Edge Length of Octahedron/2

## < 9 Radius of Octahedron Calculators

Insphere Radius of Octahedron given Total Surface Area
Insphere Radius of Octahedron = sqrt(Total Surface Area of Octahedron/(2*sqrt(3)))/sqrt(6)
Circumsphere Radius of Octahedron given Insphere Radius
Circumsphere Radius of Octahedron = sqrt(3)*Insphere Radius of Octahedron
Midsphere Radius of Octahedron given Space Diagonal
Midsphere Radius of Octahedron = Space Diagonal of Octahedron/(2*sqrt(2))
Insphere Radius of Octahedron given Midsphere Radius
Insphere Radius of Octahedron = sqrt(2/3)*Midsphere Radius of Octahedron
Midsphere Radius of Octahedron given Insphere Radius
Midsphere Radius of Octahedron = sqrt(3/2)*Insphere Radius of Octahedron
Circumsphere Radius of Octahedron
Circumsphere Radius of Octahedron = Edge Length of Octahedron/sqrt(2)
Insphere Radius of Octahedron
Insphere Radius of Octahedron = Edge Length of Octahedron/sqrt(6)
Circumsphere Radius of Octahedron given Space Diagonal
Circumsphere Radius of Octahedron = Space Diagonal of Octahedron/2
Midsphere Radius of Octahedron
Midsphere Radius of Octahedron = Edge Length of Octahedron/2

## Midsphere Radius of Octahedron given Insphere Radius Formula

Midsphere Radius of Octahedron = sqrt(3/2)*Insphere Radius of Octahedron
rm = sqrt(3/2)*ri

## What is an Octahedron?

An Octahedron is a symmetric and closed three dimensional shape with 8 identical equilateral triangular faces. It is a Platonic solid, which has 8 faces, 6 vertices and 12 edges. At each vertex, four equilateral triangular faces meet and at each edge, two equilateral triangular faces meet.

## What are Platonic Solids?

In three-dimensional space, a Platonic solid is a regular, convex polyhedron. It is constructed by congruent (identical in shape and size), regular (all angles equal and all sides equal), polygonal faces with the same number of faces meeting at each vertex. Five solids who meet this criteria are Tetrahedron {3,3} , Cube {4,3} , Octahedron {3,4} , Dodecahedron {5,3} , Icosahedron {3,5} ; where in {p, q}, p represents the number of edges in a face and q represents the number of edges meeting at a vertex; {p, q} is the Schläfli symbol.

## How to Calculate Midsphere Radius of Octahedron given Insphere Radius?

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

How to calculate Midsphere Radius of Octahedron given Insphere Radius using this online calculator? To use this online calculator for Midsphere Radius of Octahedron given Insphere Radius, enter Insphere Radius of Octahedron (ri) and hit the calculate button. Here is how the Midsphere Radius of Octahedron given Insphere Radius calculation can be explained with given input values -> 4.898979 = sqrt(3/2)*4.

### FAQ

What is Midsphere Radius of Octahedron given Insphere Radius?
Midsphere Radius of Octahedron given Insphere Radius formula is defined as the radius of the sphere for which all the edges of the Octahedron become a tangent line on that sphere, and is calculated using the insphere radius of the Octahedron and is represented as rm = sqrt(3/2)*ri or Midsphere Radius of Octahedron = sqrt(3/2)*Insphere Radius of Octahedron. Insphere Radius of Octahedron is the radius of the sphere that is contained by the Octahedron in such a way that all the faces are just touching the sphere.
How to calculate Midsphere Radius of Octahedron given Insphere Radius?
Midsphere Radius of Octahedron given Insphere Radius formula is defined as the radius of the sphere for which all the edges of the Octahedron become a tangent line on that sphere, and is calculated using the insphere radius of the Octahedron is calculated using Midsphere Radius of Octahedron = sqrt(3/2)*Insphere Radius of Octahedron. To calculate Midsphere Radius of Octahedron given Insphere Radius, you need Insphere Radius of Octahedron (ri). With our tool, you need to enter the respective value for Insphere Radius of 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 Midsphere Radius of Octahedron?
In this formula, Midsphere Radius of Octahedron uses Insphere Radius of Octahedron. We can use 8 other way(s) to calculate the same, which is/are as follows -
• Midsphere Radius of Octahedron = Edge Length of Octahedron/2
• Midsphere Radius of Octahedron = Circumsphere Radius of Octahedron/sqrt(2)
• Midsphere Radius of Octahedron = (3*sqrt(6))/(2*Surface to Volume Ratio of Octahedron)
• Midsphere Radius of Octahedron = Space Diagonal of Octahedron/(2*sqrt(2))
• Midsphere Radius of Octahedron = sqrt(Total Surface Area of Octahedron/(2*sqrt(3)))/2
• Midsphere Radius of Octahedron = ((3*Volume of Octahedron)/sqrt(2))^(1/3)/2
• Midsphere Radius of Octahedron = Edge Length of Octahedron/2
• Midsphere Radius of Octahedron = Space Diagonal of Octahedron/(2*sqrt(2))
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