Insphere Radius of Tetrahedron Calculator

✖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 [l_e]

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✖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.ⓘ Insphere Radius of Tetrahedron [r_i]

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Insphere Radius of Tetrahedron Solution

STEP 0: Pre-Calculation Summary

Formula Used

Insphere Radius of Tetrahedron = Edge Length of Tetrahedron/(2*sqrt(6))
r_i = l_e/(2*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 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.
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.

STEP 1: Convert Input(s) to Base Unit

Edge Length of Tetrahedron: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = l_e/(2*sqrt(6)) --> 10/(2*sqrt(6))

Evaluating ... ...

r_i = 2.04124145231932

STEP 3: Convert Result to Output's Unit

2.04124145231932 Meter --> No Conversion Required

FINAL ANSWER

2.04124145231932 ≈ 2.041241 Meter <-- Insphere Radius of Tetrahedron

(Calculation completed in 00.004 seconds)

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< Insphere Radius of Tetrahedron Calculators

Insphere Radius of Tetrahedron given Face Area

LaTeX Go Insphere Radius of Tetrahedron = sqrt((4*Face Area of Tetrahedron)/sqrt(3))/(2*sqrt(6))

Insphere Radius of Tetrahedron

LaTeX Go Insphere Radius of Tetrahedron = Edge Length of Tetrahedron/(2*sqrt(6))

Insphere Radius of Tetrahedron given Circumsphere Radius

LaTeX Go Insphere Radius of Tetrahedron = Circumsphere Radius of Tetrahedron/3

Insphere Radius of Tetrahedron given Height

LaTeX Go Insphere Radius of Tetrahedron = Height of Tetrahedron/4

< Radius of Tetrahedron Calculators

Insphere Radius of Tetrahedron given Face Area

LaTeX Go Insphere Radius of Tetrahedron = sqrt((4*Face Area of Tetrahedron)/sqrt(3))/(2*sqrt(6))

Circumsphere Radius of Tetrahedron

LaTeX Go Circumsphere Radius of Tetrahedron = 1/2*sqrt(3/2)*Edge Length of Tetrahedron

Midsphere Radius of Tetrahedron

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

Insphere Radius of Tetrahedron

LaTeX Go Insphere Radius of Tetrahedron = Edge Length of Tetrahedron/(2*sqrt(6))

Insphere Radius of Tetrahedron Formula

LaTeX Go

Insphere Radius of Tetrahedron = Edge Length of Tetrahedron/(2*sqrt(6))
r_i = l_e/(2*sqrt(6))

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 Insphere Radius of Tetrahedron?

Insphere Radius of Tetrahedron calculator uses Insphere Radius of Tetrahedron = Edge Length of Tetrahedron/(2*sqrt(6)) to calculate the Insphere Radius of Tetrahedron, Insphere Radius of Tetrahedron formula is defined as the radius of the sphere that is contained by the Tetrahedron in such a way that all the faces just touching the sphere. Insphere Radius of Tetrahedron is denoted by r_i symbol.

How to calculate Insphere Radius of Tetrahedron using this online calculator? To use this online calculator for Insphere Radius of Tetrahedron, enter Edge Length of Tetrahedron (l_e) and hit the calculate button. Here is how the Insphere Radius of Tetrahedron calculation can be explained with given input values -> 2.041241 = 10/(2*sqrt(6)).

FAQ

What is Insphere Radius of Tetrahedron?

Insphere Radius of Tetrahedron formula is defined as the radius of the sphere that is contained by the Tetrahedron in such a way that all the faces just touching the sphere and is represented as r_i = l_e/(2*sqrt(6)) or Insphere Radius of Tetrahedron = Edge Length of Tetrahedron/(2*sqrt(6)). 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.

How to calculate Insphere Radius of Tetrahedron?

Insphere Radius of Tetrahedron formula is defined as the radius of the sphere that is contained by the Tetrahedron in such a way that all the faces just touching the sphere is calculated using Insphere Radius of Tetrahedron = Edge Length of Tetrahedron/(2*sqrt(6)). To calculate Insphere Radius of Tetrahedron, you need Edge Length of Tetrahedron (l_e). With our tool, you need to enter the respective value for Edge Length 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 Insphere Radius of Tetrahedron?

In this formula, Insphere Radius of Tetrahedron uses Edge Length of Tetrahedron. We can use 3 other way(s) to calculate the same, which is/are as follows -

Insphere Radius of Tetrahedron = sqrt((4*Face Area of Tetrahedron)/sqrt(3))/(2*sqrt(6))
Insphere Radius of Tetrahedron = Height of Tetrahedron/4
Insphere Radius of Tetrahedron = Circumsphere Radius of Tetrahedron/3

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