Insphere Radius of Octahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Insphere Radius of Octahedron = sqrt(2/3)*Midsphere Radius of Octahedron
ri = sqrt(2/3)*rm
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 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.
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.
STEP 1: Convert Input(s) to Base Unit
Midsphere Radius of Octahedron: 5 Meter --> 5 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ri = sqrt(2/3)*rm --> sqrt(2/3)*5
Evaluating ... ...
ri = 4.08248290463863
STEP 3: Convert Result to Output's Unit
4.08248290463863 Meter --> No Conversion Required
FINAL ANSWER
4.08248290463863 4.082483 Meter <-- Insphere Radius of Octahedron
(Calculation completed in 00.005 seconds)

Credits

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Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
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Insphere Radius of Octahedron Calculators

Insphere Radius of Octahedron given Circumsphere Radius
​ LaTeX ​ Go Insphere Radius of Octahedron = Circumsphere Radius of Octahedron/sqrt(3)
Insphere Radius of Octahedron given Midsphere Radius
​ LaTeX ​ Go Insphere Radius of Octahedron = sqrt(2/3)*Midsphere Radius of Octahedron
Insphere Radius of Octahedron given Space Diagonal
​ LaTeX ​ Go Insphere Radius of Octahedron = Space Diagonal of Octahedron/(2*sqrt(3))
Insphere Radius of Octahedron
​ LaTeX ​ Go Insphere Radius of Octahedron = Edge Length of Octahedron/sqrt(6)

Radius of Octahedron Calculators

Circumsphere Radius of Octahedron given Insphere Radius
​ LaTeX ​ Go Circumsphere Radius of Octahedron = sqrt(3)*Insphere Radius of Octahedron
Insphere Radius of Octahedron given Midsphere Radius
​ LaTeX ​ Go Insphere Radius of Octahedron = sqrt(2/3)*Midsphere Radius of Octahedron
Circumsphere Radius of Octahedron
​ LaTeX ​ Go Circumsphere Radius of Octahedron = Edge Length of Octahedron/sqrt(2)
Insphere Radius of Octahedron
​ LaTeX ​ Go Insphere Radius of Octahedron = Edge Length of Octahedron/sqrt(6)

Insphere Radius of Octahedron given Midsphere Radius Formula

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

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 Insphere Radius of Octahedron given Midsphere Radius?

Insphere Radius of Octahedron given Midsphere Radius calculator uses Insphere Radius of Octahedron = sqrt(2/3)*Midsphere Radius of Octahedron to calculate the Insphere Radius of Octahedron, Insphere Radius of Octahedron given Midsphere Radius formula is defined as the radius of the sphere that is contained by the Octahedron in such a way that all the faces just touch the sphere, and is calculated using the midsphere radius of the Octahedron. Insphere Radius of Octahedron is denoted by ri symbol.

How to calculate Insphere Radius of Octahedron given Midsphere Radius using this online calculator? To use this online calculator for Insphere Radius of Octahedron given Midsphere Radius, enter Midsphere Radius of Octahedron (rm) and hit the calculate button. Here is how the Insphere Radius of Octahedron given Midsphere Radius calculation can be explained with given input values -> 4.082483 = sqrt(2/3)*5.

FAQ

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