Insphere Radius of Octahedron given Volume Calculator

✖Volume of Octahedron is the total quantity of three dimensional space enclosed by the entire surface of the Octahedron.ⓘ Volume of Octahedron [V]

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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 Volume [r_i]

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Insphere Radius of Octahedron given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Insphere Radius of Octahedron = ((3*Volume of Octahedron)/sqrt(2))^(1/3)/sqrt(6)
r_i = ((3*V)/sqrt(2))^(1/3)/sqrt(6)
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.
Volume of Octahedron - (Measured in Cubic Meter) - Volume of Octahedron is the total quantity of three dimensional space enclosed by the entire surface of the Octahedron.

STEP 1: Convert Input(s) to Base Unit

Volume of Octahedron: 470 Cubic Meter --> 470 Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = ((3*V)/sqrt(2))^(1/3)/sqrt(6) --> ((3*470)/sqrt(2))^(1/3)/sqrt(6)

Evaluating ... ...

r_i = 4.07842436896281

STEP 3: Convert Result to Output's Unit

4.07842436896281 Meter --> No Conversion Required

FINAL ANSWER

4.07842436896281 ≈ 4.078424 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 Volume Formula

LaTeX Go

Insphere Radius of Octahedron = ((3*Volume of Octahedron)/sqrt(2))^(1/3)/sqrt(6)
r_i = ((3*V)/sqrt(2))^(1/3)/sqrt(6)

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 Volume?

Insphere Radius of Octahedron given Volume calculator uses Insphere Radius of Octahedron = ((3*Volume of Octahedron)/sqrt(2))^(1/3)/sqrt(6) to calculate the Insphere Radius of Octahedron, Insphere Radius of Octahedron given Volume 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 volume of the Octahedron. Insphere Radius of Octahedron is denoted by r_i symbol.

How to calculate Insphere Radius of Octahedron given Volume using this online calculator? To use this online calculator for Insphere Radius of Octahedron given Volume, enter Volume of Octahedron (V) and hit the calculate button. Here is how the Insphere Radius of Octahedron given Volume calculation can be explained with given input values -> 4.078424 = ((3*470)/sqrt(2))^(1/3)/sqrt(6).

FAQ

What is Insphere Radius of Octahedron given Volume?

Insphere Radius of Octahedron given Volume 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 volume of the Octahedron and is represented as r_i = ((3*V)/sqrt(2))^(1/3)/sqrt(6) or Insphere Radius of Octahedron = ((3*Volume of Octahedron)/sqrt(2))^(1/3)/sqrt(6). Volume of Octahedron is the total quantity of three dimensional space enclosed by the entire surface of the Octahedron.

How to calculate Insphere Radius of Octahedron given Volume?

Insphere Radius of Octahedron given Volume 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 volume of the Octahedron is calculated using Insphere Radius of Octahedron = ((3*Volume of Octahedron)/sqrt(2))^(1/3)/sqrt(6). To calculate Insphere Radius of Octahedron given Volume, you need Volume of Octahedron (V). With our tool, you need to enter the respective value for Volume 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 Volume 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 = Space Diagonal of Octahedron/(2*sqrt(3))

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