Edge Length of Tetrahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
Edge Length of Tetrahedron = 2*sqrt(6)*Insphere Radius of Tetrahedron
le = 2*sqrt(6)*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
Edge Length of Tetrahedron - (Measured in Meter) - Edge Length of Tetrahedron is the length of any of edges of the Tetrahedron or the distance between any pair of adjacent vertices of the Tetrahedron.
Insphere Radius of Tetrahedron - (Measured in Meter) - Insphere Radius of Tetrahedron is the radius of the sphere that is contained by the Tetrahedron in such a way that all the faces just touching the sphere.
STEP 1: Convert Input(s) to Base Unit
Insphere Radius of Tetrahedron: 2 Meter --> 2 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
le = 2*sqrt(6)*ri --> 2*sqrt(6)*2
Evaluating ... ...
le = 9.79795897113271
STEP 3: Convert Result to Output's Unit
9.79795897113271 Meter --> No Conversion Required
FINAL ANSWER
9.79795897113271 9.797959 Meter <-- Edge Length of Tetrahedron
(Calculation completed in 00.020 seconds)

Credits

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Created by Dhruv Walia
Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
Dhruv Walia has created this Calculator and 1100+ more calculators!
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Verified by Nikhil
Mumbai University (DJSCE), Mumbai
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8 Edge Length of Tetrahedron Calculators

Edge Length of Tetrahedron given Total Surface Area
​ Go Edge Length of Tetrahedron = sqrt(Total Surface Area of Tetrahedron/(sqrt(3)))
Edge Length of Tetrahedron given Face Area
​ Go Edge Length of Tetrahedron = sqrt((4*Face Area of Tetrahedron)/sqrt(3))
Edge Length of Tetrahedron given Surface to Volume Ratio
​ Go Edge Length of Tetrahedron = (6*sqrt(6))/Surface to Volume Ratio of Tetrahedron
Edge Length of Tetrahedron given Circumsphere Radius
​ Go Edge Length of Tetrahedron = 2*sqrt(2/3)*Circumsphere Radius of Tetrahedron
Edge Length of Tetrahedron given Midsphere Radius
​ Go Edge Length of Tetrahedron = 2*sqrt(2)*Midsphere Radius of Tetrahedron
Edge Length of Tetrahedron given Insphere Radius
​ Go Edge Length of Tetrahedron = 2*sqrt(6)*Insphere Radius of Tetrahedron
Edge Length of Tetrahedron given Volume
​ Go Edge Length of Tetrahedron = (6*sqrt(2)*Volume of Tetrahedron)^(1/3)
Edge Length of Tetrahedron given Height
​ Go Edge Length of Tetrahedron = sqrt(3/2)*Height of Tetrahedron

Edge Length of Tetrahedron given Insphere Radius Formula

Edge Length of Tetrahedron = 2*sqrt(6)*Insphere Radius of Tetrahedron
le = 2*sqrt(6)*ri

What is a Tetrahedron?

A Tetrahedron is a symmetric and closed three dimensional shape with 4 identical equilateral triangular faces. It is a Platonic solid, which has 4 faces, 4 vertices and 6 edges. At each vertex, three 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 Edge Length of Tetrahedron given Insphere Radius?

Edge Length of Tetrahedron given Insphere Radius calculator uses Edge Length of Tetrahedron = 2*sqrt(6)*Insphere Radius of Tetrahedron to calculate the Edge Length of Tetrahedron, The Edge Length of Tetrahedron given Insphere Radius formula is defined as the length of any of edges of the Tetrahedron or the distance between any pair of adjacent vertices of the Tetrahedron, and calculated using the insphere radius of the Tetrahedron. Edge Length of Tetrahedron is denoted by le symbol.

How to calculate Edge Length of Tetrahedron given Insphere Radius using this online calculator? To use this online calculator for Edge Length of Tetrahedron given Insphere Radius, enter Insphere Radius of Tetrahedron (ri) and hit the calculate button. Here is how the Edge Length of Tetrahedron given Insphere Radius calculation can be explained with given input values -> 9.797959 = 2*sqrt(6)*2.

FAQ

What is Edge Length of Tetrahedron given Insphere Radius?
The Edge Length of Tetrahedron given Insphere Radius formula is defined as the length of any of edges of the Tetrahedron or the distance between any pair of adjacent vertices of the Tetrahedron, and calculated using the insphere radius of the Tetrahedron and is represented as le = 2*sqrt(6)*ri or Edge Length of Tetrahedron = 2*sqrt(6)*Insphere Radius of Tetrahedron. Insphere Radius of Tetrahedron is the radius of the sphere that is contained by the Tetrahedron in such a way that all the faces just touching the sphere.
How to calculate Edge Length of Tetrahedron given Insphere Radius?
The Edge Length of Tetrahedron given Insphere Radius formula is defined as the length of any of edges of the Tetrahedron or the distance between any pair of adjacent vertices of the Tetrahedron, and calculated using the insphere radius of the Tetrahedron is calculated using Edge Length of Tetrahedron = 2*sqrt(6)*Insphere Radius of Tetrahedron. To calculate Edge Length of Tetrahedron given Insphere Radius, you need Insphere Radius of Tetrahedron (ri). With our tool, you need to enter the respective value for Insphere Radius of Tetrahedron 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 Edge Length of Tetrahedron?
In this formula, Edge Length of Tetrahedron uses Insphere Radius of Tetrahedron. We can use 7 other way(s) to calculate the same, which is/are as follows -
  • Edge Length of Tetrahedron = sqrt(Total Surface Area of Tetrahedron/(sqrt(3)))
  • Edge Length of Tetrahedron = sqrt((4*Face Area of Tetrahedron)/sqrt(3))
  • Edge Length of Tetrahedron = sqrt(3/2)*Height of Tetrahedron
  • Edge Length of Tetrahedron = 2*sqrt(2)*Midsphere Radius of Tetrahedron
  • Edge Length of Tetrahedron = 2*sqrt(2/3)*Circumsphere Radius of Tetrahedron
  • Edge Length of Tetrahedron = (6*sqrt(6))/Surface to Volume Ratio of Tetrahedron
  • Edge Length of Tetrahedron = (6*sqrt(2)*Volume of Tetrahedron)^(1/3)
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