Edge Length of Tetrahedron given Midsphere Radius Calculator

✖Midsphere Radius of Tetrahedron is the radius of the sphere for which all the edges of the Tetrahedron become a tangent line to that sphere.ⓘ Midsphere Radius of Tetrahedron [r_m]

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✖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.ⓘ Edge Length of Tetrahedron given Midsphere Radius [l_e]

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Edge Length of Tetrahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Edge Length of Tetrahedron = 2*sqrt(2)*Midsphere Radius of Tetrahedron
l_e = 2*sqrt(2)*r_m
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.
Midsphere Radius of Tetrahedron - (Measured in Meter) - Midsphere Radius of Tetrahedron is the radius of the sphere for which all the edges of the Tetrahedron become a tangent line to that sphere.

STEP 1: Convert Input(s) to Base Unit

Midsphere Radius of Tetrahedron: 4 Meter --> 4 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e = 2*sqrt(2)*r_m --> 2*sqrt(2)*4

Evaluating ... ...

l_e = 11.3137084989848

STEP 3: Convert Result to Output's Unit

11.3137084989848 Meter --> No Conversion Required

FINAL ANSWER

11.3137084989848 ≈ 11.31371 Meter <-- Edge Length of Tetrahedron

(Calculation completed in 00.004 seconds)

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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

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< Edge Length of Tetrahedron Calculators

Edge Length of Tetrahedron given Total Surface Area

LaTeX Go Edge Length of Tetrahedron = sqrt(Total Surface Area of Tetrahedron/(sqrt(3)))

Edge Length of Tetrahedron given Face Area

LaTeX Go Edge Length of Tetrahedron = sqrt((4*Face Area of Tetrahedron)/sqrt(3))

Edge Length of Tetrahedron given Midsphere Radius

LaTeX Go Edge Length of Tetrahedron = 2*sqrt(2)*Midsphere Radius of Tetrahedron

Edge Length of Tetrahedron given Height

LaTeX Go Edge Length of Tetrahedron = sqrt(3/2)*Height of Tetrahedron

Edge Length of Tetrahedron given Midsphere Radius Formula

LaTeX Go

Edge Length of Tetrahedron = 2*sqrt(2)*Midsphere Radius of Tetrahedron
l_e = 2*sqrt(2)*r_m

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 Midsphere Radius?

Edge Length of Tetrahedron given Midsphere Radius calculator uses Edge Length of Tetrahedron = 2*sqrt(2)*Midsphere Radius of Tetrahedron to calculate the Edge Length of Tetrahedron, The Edge Length of Tetrahedron given Midsphere 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 midsphere radius of the Tetrahedron. Edge Length of Tetrahedron is denoted by l_e symbol.

How to calculate Edge Length of Tetrahedron given Midsphere Radius using this online calculator? To use this online calculator for Edge Length of Tetrahedron given Midsphere Radius, enter Midsphere Radius of Tetrahedron (r_m) and hit the calculate button. Here is how the Edge Length of Tetrahedron given Midsphere Radius calculation can be explained with given input values -> 11.31371 = 2*sqrt(2)*4.

FAQ

What is Edge Length of Tetrahedron given Midsphere Radius?

The Edge Length of Tetrahedron given Midsphere 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 midsphere radius of the Tetrahedron and is represented as l_e = 2*sqrt(2)*r_m or Edge Length of Tetrahedron = 2*sqrt(2)*Midsphere Radius of Tetrahedron. Midsphere Radius of Tetrahedron is the radius of the sphere for which all the edges of the Tetrahedron become a tangent line to that sphere.

How to calculate Edge Length of Tetrahedron given Midsphere Radius?

The Edge Length of Tetrahedron given Midsphere 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 midsphere radius of the Tetrahedron is calculated using Edge Length of Tetrahedron = 2*sqrt(2)*Midsphere Radius of Tetrahedron. To calculate Edge Length of Tetrahedron given Midsphere Radius, you need Midsphere Radius of Tetrahedron (r_m). With our tool, you need to enter the respective value for Midsphere 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 Midsphere Radius of Tetrahedron. We can use 3 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

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