Midsphere Radius of Tetrahedron given Volume 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 given Volume [r_m]

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Formula

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Midsphere Radius of Tetrahedron given Volume

Formula

`"r"_{"m"} = (6*sqrt(2)*"V")^(1/3)/(2*sqrt(2))`

Example

`"3.556893m"=(6*sqrt(2)*"120m³")^(1/3)/(2*sqrt(2))`

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Midsphere Radius of Tetrahedron given Volume Solution

STEP 0: Pre-Calculation Summary

Formula Used

Midsphere Radius of Tetrahedron = (6*sqrt(2)*Volume of Tetrahedron)^(1/3)/(2*sqrt(2))
r_m = (6*sqrt(2)*V)^(1/3)/(2*sqrt(2))
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

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.
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

r_m = (6*sqrt(2)*V)^(1/3)/(2*sqrt(2)) --> (6*sqrt(2)*120)^(1/3)/(2*sqrt(2))

Evaluating ... ...

r_m = 3.55689330449006

STEP 3: Convert Result to Output's Unit

3.55689330449006 Meter --> No Conversion Required

FINAL ANSWER

3.55689330449006 ≈ 3.556893 Meter <-- Midsphere Radius of Tetrahedron

(Calculation completed in 00.004 seconds)

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Credits

Created by Divanshi Jain

Netaji Subhash University of Technology, Delhi (NSUT Delhi), Dwarka

Divanshi Jain has created this Calculator and 300+ more calculators!

Verified by Dhruv Walia

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

Dhruv Walia has verified this Calculator and 400+ more calculators!

< 8 Midsphere Radius of Tetrahedron Calculators

Midsphere Radius of Tetrahedron given Total Surface Area

Go Midsphere Radius of Tetrahedron = sqrt(Total Surface Area of Tetrahedron/(sqrt(3)))/(2*sqrt(2))

Midsphere Radius of Tetrahedron given Face Area

Go Midsphere Radius of Tetrahedron = sqrt((4*Face Area of Tetrahedron)/sqrt(3))/(2*sqrt(2))

Midsphere Radius of Tetrahedron given Volume

Go Midsphere Radius of Tetrahedron = (6*sqrt(2)*Volume of Tetrahedron)^(1/3)/(2*sqrt(2))

Midsphere Radius of Tetrahedron given Height

Go Midsphere Radius of Tetrahedron = sqrt(3/2)*Height of Tetrahedron/(2*sqrt(2))

Midsphere Radius of Tetrahedron given Surface to Volume Ratio

Go Midsphere Radius of Tetrahedron = (3*sqrt(3))/Surface to Volume Ratio of Tetrahedron

Midsphere Radius of Tetrahedron given Circumsphere Radius

Go Midsphere Radius of Tetrahedron = sqrt(1/3)*Circumsphere Radius of Tetrahedron

Midsphere Radius of Tetrahedron given Insphere Radius

Go Midsphere Radius of Tetrahedron = sqrt(3)*Insphere Radius of Tetrahedron

Midsphere Radius of Tetrahedron

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

Midsphere Radius of Tetrahedron given Volume Formula

Midsphere Radius of Tetrahedron = (6*sqrt(2)*Volume of Tetrahedron)^(1/3)/(2*sqrt(2))
r_m = (6*sqrt(2)*V)^(1/3)/(2*sqrt(2))

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 Midsphere Radius of Tetrahedron given Volume?

Midsphere Radius of Tetrahedron given Volume calculator uses Midsphere Radius of Tetrahedron = (6*sqrt(2)*Volume of Tetrahedron)^(1/3)/(2*sqrt(2)) to calculate the Midsphere Radius of Tetrahedron, The Midsphere Radius of Tetrahedron given Volume formula is defined as the radius of the sphere for which all the edges of the Tetrahedron become a tangent line to that sphere, calculated using volume of Tetrahedron. Midsphere Radius of Tetrahedron is denoted by r_m symbol.

How to calculate Midsphere Radius of Tetrahedron given Volume using this online calculator? To use this online calculator for Midsphere Radius of Tetrahedron given Volume, enter Volume of Tetrahedron (V) and hit the calculate button. Here is how the Midsphere Radius of Tetrahedron given Volume calculation can be explained with given input values -> 3.556893 = (6*sqrt(2)*120)^(1/3)/(2*sqrt(2)).

FAQ

What is Midsphere Radius of Tetrahedron given Volume?

The Midsphere Radius of Tetrahedron given Volume formula is defined as the radius of the sphere for which all the edges of the Tetrahedron become a tangent line to that sphere, calculated using volume of Tetrahedron and is represented as r_m = (6*sqrt(2)*V)^(1/3)/(2*sqrt(2)) or Midsphere Radius of Tetrahedron = (6*sqrt(2)*Volume of Tetrahedron)^(1/3)/(2*sqrt(2)). Volume of Tetrahedron is the total quantity of three dimensional space enclosed by the surface of the Tetrahedron.

How to calculate Midsphere Radius of Tetrahedron given Volume?

The Midsphere Radius of Tetrahedron given Volume formula is defined as the radius of the sphere for which all the edges of the Tetrahedron become a tangent line to that sphere, calculated using volume of Tetrahedron is calculated using Midsphere Radius of Tetrahedron = (6*sqrt(2)*Volume of Tetrahedron)^(1/3)/(2*sqrt(2)). To calculate Midsphere 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 Midsphere Radius of Tetrahedron?

In this formula, Midsphere Radius of Tetrahedron uses Volume of Tetrahedron. We can use 7 other way(s) to calculate the same, which is/are as follows -

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

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