Circumsphere Radius of Octahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Circumsphere Radius of Octahedron = sqrt(3)*Insphere Radius of Octahedron
rc = sqrt(3)*ri
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
Circumsphere Radius of Octahedron - (Measured in Meter) - Circumsphere Radius of Octahedron is the radius of the sphere that contains the Octahedron in such a way that all the vertices are lying on the 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
rc = sqrt(3)*ri --> sqrt(3)*4
Evaluating ... ...
rc = 6.92820323027551
STEP 3: Convert Result to Output's Unit
6.92820323027551 Meter --> No Conversion Required
FINAL ANSWER
6.92820323027551 6.928203 Meter <-- Circumsphere Radius of Octahedron
(Calculation completed in 00.020 seconds)

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St Joseph's College (SJC), Bengaluru
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Vellore Institute of Technology (VIT), Bhopal
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7 Circumsphere Radius of Octahedron Calculators

Circumsphere Radius of Octahedron given Total Surface Area
​ Go Circumsphere Radius of Octahedron = sqrt(Total Surface Area of Octahedron/(4*sqrt(3)))
Circumsphere Radius of Octahedron given Volume
​ Go Circumsphere Radius of Octahedron = ((3*Volume of Octahedron)/sqrt(2))^(1/3)/sqrt(2)
Circumsphere Radius of Octahedron given Surface to Volume Ratio
​ Go Circumsphere Radius of Octahedron = (3*sqrt(3))/Surface to Volume Ratio of Octahedron
Circumsphere Radius of Octahedron given Midsphere Radius
​ Go Circumsphere Radius of Octahedron = sqrt(2)*Midsphere Radius of Octahedron
Circumsphere Radius of Octahedron given Insphere Radius
​ Go Circumsphere Radius of Octahedron = sqrt(3)*Insphere Radius of Octahedron
Circumsphere Radius of Octahedron
​ Go Circumsphere Radius of Octahedron = Edge Length of Octahedron/sqrt(2)
Circumsphere Radius of Octahedron given Space Diagonal
​ Go Circumsphere Radius of Octahedron = Space Diagonal of Octahedron/2

9 Radius of Octahedron Calculators

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

Circumsphere Radius of Octahedron given Insphere Radius Formula

Circumsphere Radius of Octahedron = sqrt(3)*Insphere Radius of Octahedron
rc = 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 Circumsphere Radius of Octahedron given Insphere Radius?

Circumsphere Radius of Octahedron given Insphere Radius calculator uses Circumsphere Radius of Octahedron = sqrt(3)*Insphere Radius of Octahedron to calculate the Circumsphere Radius of Octahedron, Circumsphere Radius of Octahedron given Insphere Radius formula is defined as the radius of the sphere that contains the Octahedron in such a way that all the vertices are lying on the sphere, and calculated using the insphere radius of the Octahedron. Circumsphere Radius of Octahedron is denoted by rc symbol.

How to calculate Circumsphere Radius of Octahedron given Insphere Radius using this online calculator? To use this online calculator for Circumsphere Radius of Octahedron given Insphere Radius, enter Insphere Radius of Octahedron (ri) and hit the calculate button. Here is how the Circumsphere Radius of Octahedron given Insphere Radius calculation can be explained with given input values -> 6.928203 = sqrt(3)*4.

FAQ

What is Circumsphere Radius of Octahedron given Insphere Radius?
Circumsphere Radius of Octahedron given Insphere Radius formula is defined as the radius of the sphere that contains the Octahedron in such a way that all the vertices are lying on the sphere, and calculated using the insphere radius of the Octahedron and is represented as rc = sqrt(3)*ri or Circumsphere Radius of Octahedron = 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 Circumsphere Radius of Octahedron given Insphere Radius?
Circumsphere Radius of Octahedron given Insphere Radius formula is defined as the radius of the sphere that contains the Octahedron in such a way that all the vertices are lying on the sphere, and calculated using the insphere radius of the Octahedron is calculated using Circumsphere Radius of Octahedron = sqrt(3)*Insphere Radius of Octahedron. To calculate Circumsphere 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 Circumsphere Radius of Octahedron?
In this formula, Circumsphere Radius of Octahedron uses Insphere Radius of Octahedron. We can use 8 other way(s) to calculate the same, which is/are as follows -
  • Circumsphere Radius of Octahedron = Edge Length of Octahedron/sqrt(2)
  • Circumsphere Radius of Octahedron = sqrt(2)*Midsphere Radius of Octahedron
  • Circumsphere Radius of Octahedron = sqrt(Total Surface Area of Octahedron/(4*sqrt(3)))
  • Circumsphere Radius of Octahedron = (3*sqrt(3))/Surface to Volume Ratio of Octahedron
  • Circumsphere Radius of Octahedron = Space Diagonal of Octahedron/2
  • Circumsphere Radius of Octahedron = ((3*Volume of Octahedron)/sqrt(2))^(1/3)/sqrt(2)
  • Circumsphere Radius of Octahedron = Edge Length of Octahedron/sqrt(2)
  • Circumsphere Radius of Octahedron = Space Diagonal of Octahedron/2
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