## Insphere Radius of Tetrahedron given Volume Solution

STEP 0: Pre-Calculation Summary
Formula Used
Insphere Radius of Tetrahedron = (6*sqrt(2)*Volume of Tetrahedron)^(1/3)/(2*sqrt(6))
ri = (6*sqrt(2)*V)^(1/3)/(2*sqrt(6))
This formula uses 1 Functions, 2 Variables
Functions Used
sqrt - Square root function, 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.
Volume of Tetrahedron - (Measured in Cubic Meter) - Volume of Tetrahedron is the total quantity of three dimensional space enclosed by the surface of the Tetrahedron.
STEP 1: Convert Input(s) to Base Unit
Volume of Tetrahedron: 120 Cubic Meter --> 120 Cubic Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ri = (6*sqrt(2)*V)^(1/3)/(2*sqrt(6)) --> (6*sqrt(2)*120)^(1/3)/(2*sqrt(6))
Evaluating ... ...
ri = 2.05357330682612
STEP 3: Convert Result to Output's Unit
2.05357330682612 Meter --> No Conversion Required
2.05357330682612 2.053573 Meter <-- Insphere Radius of Tetrahedron
(Calculation completed in 00.003 seconds)
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## Credits

Created by Divanshi Jain
Netaji Subhash University of Technology, Delhi (NSUT Delhi), Dwarka
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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
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## < 8 Insphere Radius of Tetrahedron Calculators

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

## Insphere Radius of Tetrahedron given Volume Formula

Insphere Radius of Tetrahedron = (6*sqrt(2)*Volume of Tetrahedron)^(1/3)/(2*sqrt(6))
ri = (6*sqrt(2)*V)^(1/3)/(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 given Volume?

Insphere Radius of Tetrahedron given Volume calculator uses Insphere Radius of Tetrahedron = (6*sqrt(2)*Volume of Tetrahedron)^(1/3)/(2*sqrt(6)) to calculate the Insphere Radius of Tetrahedron, The Insphere Radius of Tetrahedron given Volume 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, calculated using volume of Tetrahedron. Insphere Radius of Tetrahedron is denoted by ri symbol.

How to calculate Insphere Radius of Tetrahedron given Volume using this online calculator? To use this online calculator for Insphere Radius of Tetrahedron given Volume, enter Volume of Tetrahedron (V) and hit the calculate button. Here is how the Insphere Radius of Tetrahedron given Volume calculation can be explained with given input values -> 2.053573 = (6*sqrt(2)*120)^(1/3)/(2*sqrt(6)).

### FAQ

What is Insphere Radius of Tetrahedron given Volume?
The Insphere Radius of Tetrahedron given Volume 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, calculated using volume of Tetrahedron and is represented as ri = (6*sqrt(2)*V)^(1/3)/(2*sqrt(6)) or Insphere Radius of Tetrahedron = (6*sqrt(2)*Volume of Tetrahedron)^(1/3)/(2*sqrt(6)). Volume of Tetrahedron is the total quantity of three dimensional space enclosed by the surface of the Tetrahedron.
How to calculate Insphere Radius of Tetrahedron given Volume?
The Insphere Radius of Tetrahedron given Volume 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, calculated using volume of Tetrahedron is calculated using Insphere Radius of Tetrahedron = (6*sqrt(2)*Volume of Tetrahedron)^(1/3)/(2*sqrt(6)). To calculate Insphere Radius of Tetrahedron given Volume, you need Volume of Tetrahedron (V). With our tool, you need to enter the respective value for Volume 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 Volume of Tetrahedron. We can use 7 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 = Edge Length of Tetrahedron/(2*sqrt(6))
• Insphere Radius of Tetrahedron = Height of Tetrahedron/4 