Insphere Radius of Octahedron given Space Diagonal Calculator

✖The Space Diagonal of Octahedron is the line connecting two vertices that are not on the same face of Octahedron.ⓘ Space Diagonal of Octahedron [d_Space]

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✖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.ⓘ Insphere Radius of Octahedron given Space Diagonal [r_i]

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Insphere Radius of Octahedron given Space Diagonal Solution

STEP 0: Pre-Calculation Summary

Formula Used

Insphere Radius of Octahedron = Space Diagonal of Octahedron/(2*sqrt(3))
r_i = d_Space/(2*sqrt(3))
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.
Space Diagonal of Octahedron - (Measured in Meter) - The Space Diagonal of Octahedron is the line connecting two vertices that are not on the same face of Octahedron.

STEP 1: Convert Input(s) to Base Unit

Space Diagonal of Octahedron: 14 Meter --> 14 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = d_Space/(2*sqrt(3)) --> 14/(2*sqrt(3))

Evaluating ... ...

r_i = 4.04145188432738

STEP 3: Convert Result to Output's Unit

4.04145188432738 Meter --> No Conversion Required

FINAL ANSWER

4.04145188432738 ≈ 4.041452 Meter <-- Insphere Radius of Octahedron

(Calculation completed in 00.004 seconds)

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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)

Insphere Radius of Octahedron given Space Diagonal Formula

LaTeX Go

Insphere Radius of Octahedron = Space Diagonal of Octahedron/(2*sqrt(3))
r_i = d_Space/(2*sqrt(3))

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 Space Diagonal?

Insphere Radius of Octahedron given Space Diagonal calculator uses Insphere Radius of Octahedron = Space Diagonal of Octahedron/(2*sqrt(3)) to calculate the Insphere Radius of Octahedron, Insphere Radius of Octahedron given Space Diagonal 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 space diagonal of the Octahedron. Insphere Radius of Octahedron is denoted by r_i symbol.

How to calculate Insphere Radius of Octahedron given Space Diagonal using this online calculator? To use this online calculator for Insphere Radius of Octahedron given Space Diagonal, enter Space Diagonal of Octahedron (d_Space) and hit the calculate button. Here is how the Insphere Radius of Octahedron given Space Diagonal calculation can be explained with given input values -> 4.041452 = 14/(2*sqrt(3)).

FAQ

What is Insphere Radius of Octahedron given Space Diagonal?

Insphere Radius of Octahedron given Space Diagonal 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 space diagonal of the Octahedron and is represented as r_i = d_Space/(2*sqrt(3)) or Insphere Radius of Octahedron = Space Diagonal of Octahedron/(2*sqrt(3)). The Space Diagonal of Octahedron is the line connecting two vertices that are not on the same face of Octahedron.

How to calculate Insphere Radius of Octahedron given Space Diagonal?

Insphere Radius of Octahedron given Space Diagonal 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 space diagonal of the Octahedron is calculated using Insphere Radius of Octahedron = Space Diagonal of Octahedron/(2*sqrt(3)). To calculate Insphere Radius of Octahedron given Space Diagonal, you need Space Diagonal of Octahedron (d_Space). With our tool, you need to enter the respective value for Space Diagonal 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 Space Diagonal 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 = sqrt(2/3)*Midsphere Radius of Octahedron
Insphere Radius of Octahedron = Circumsphere Radius of Octahedron/sqrt(3)

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