Space Diagonal of Octahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Space Diagonal of Octahedron = 2*sqrt(3)*Insphere Radius of Octahedron
dSpace = 2*sqrt(3)*ri
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - Square root function, sqrt(Number)
Variables Used
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.
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
dSpace = 2*sqrt(3)*ri --> 2*sqrt(3)*4
Evaluating ... ...
dSpace = 13.856406460551
STEP 3: Convert Result to Output's Unit
13.856406460551 Meter --> No Conversion Required
FINAL ANSWER
13.856406460551 13.85641 Meter <-- Space Diagonal of Octahedron
(Calculation completed in 00.004 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
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7 Space Diagonal of Octahedron Calculators

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

4 Space Diagonal of Octahedron Calculators

Space Diagonal of Octahedron given Volume
Go Space Diagonal of Octahedron = sqrt(2)*((3*Volume of Octahedron)/sqrt(2))^(1/3)
Space Diagonal of Octahedron given Midsphere Radius
Go Space Diagonal of Octahedron = 2*sqrt(2)*Midsphere Radius of Octahedron
Space Diagonal of Octahedron given Insphere Radius
Go Space Diagonal of Octahedron = 2*sqrt(3)*Insphere Radius of Octahedron
Space Diagonal of Octahedron
Go Space Diagonal of Octahedron = sqrt(2)*Edge Length of Octahedron

Space Diagonal of Octahedron given Insphere Radius Formula

Space Diagonal of Octahedron = 2*sqrt(3)*Insphere Radius of Octahedron
dSpace = 2*sqrt(3)*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 Space Diagonal of Octahedron given Insphere Radius?

Space Diagonal of Octahedron given Insphere Radius calculator uses Space Diagonal of Octahedron = 2*sqrt(3)*Insphere Radius of Octahedron to calculate the Space Diagonal of Octahedron, The Space Diagonal of Octahedron given Insphere Radius formula is defined as the line connecting two vertices that are not on the same face of the Octahedron, and is calculated using the insphere radius of the Octahedron. Space Diagonal of Octahedron is denoted by dSpace symbol.

How to calculate Space Diagonal of Octahedron given Insphere Radius using this online calculator? To use this online calculator for Space Diagonal of Octahedron given Insphere Radius, enter Insphere Radius of Octahedron (ri) and hit the calculate button. Here is how the Space Diagonal of Octahedron given Insphere Radius calculation can be explained with given input values -> 13.85641 = 2*sqrt(3)*4.

FAQ

What is Space Diagonal of Octahedron given Insphere Radius?
The Space Diagonal of Octahedron given Insphere Radius formula is defined as the line connecting two vertices that are not on the same face of the Octahedron, and is calculated using the insphere radius of the Octahedron and is represented as dSpace = 2*sqrt(3)*ri or Space Diagonal of Octahedron = 2*sqrt(3)*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 Space Diagonal of Octahedron given Insphere Radius?
The Space Diagonal of Octahedron given Insphere Radius formula is defined as the line connecting two vertices that are not on the same face of the Octahedron, and is calculated using the insphere radius of the Octahedron is calculated using Space Diagonal of Octahedron = 2*sqrt(3)*Insphere Radius of Octahedron. To calculate Space Diagonal 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 Space Diagonal of Octahedron?
In this formula, Space Diagonal of Octahedron uses Insphere Radius of Octahedron. We can use 9 other way(s) to calculate the same, which is/are as follows -
  • Space Diagonal of Octahedron = sqrt(2)*((3*Volume of Octahedron)/sqrt(2))^(1/3)
  • Space Diagonal of Octahedron = sqrt(2)*Edge Length of Octahedron
  • Space Diagonal of Octahedron = sqrt(Total Surface Area of Octahedron/sqrt(3))
  • Space Diagonal of Octahedron = 2*sqrt(2)*Midsphere Radius of Octahedron
  • Space Diagonal of Octahedron = (6*sqrt(3))/Surface to Volume Ratio of Octahedron
  • Space Diagonal of Octahedron = 2*Circumsphere Radius of Octahedron
  • Space Diagonal of Octahedron = sqrt(2)*Edge Length of Octahedron
  • Space Diagonal of Octahedron = 2*sqrt(2)*Midsphere Radius of Octahedron
  • Space Diagonal of Octahedron = sqrt(2)*((3*Volume of Octahedron)/sqrt(2))^(1/3)
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