Height 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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✖Height of Tetrahedron is the vertical distance from any vertex of the Tetrahedron to the face which is directly opposite to that vertex.ⓘ Height of Tetrahedron given Midsphere Radius [h]

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Height of Tetrahedron given Midsphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of Tetrahedron = 2*sqrt(4/3)*Midsphere Radius of Tetrahedron
h = 2*sqrt(4/3)*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

Height of Tetrahedron - (Measured in Meter) - Height of Tetrahedron is the vertical distance from any vertex of the Tetrahedron to the face which is directly opposite to that vertex.
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

h = 2*sqrt(4/3)*r_m --> 2*sqrt(4/3)*4

Evaluating ... ...

h = 9.23760430703401

STEP 3: Convert Result to Output's Unit

9.23760430703401 Meter --> No Conversion Required

FINAL ANSWER

9.23760430703401 ≈ 9.237604 Meter <-- Height of Tetrahedron

(Calculation completed in 00.020 seconds)

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Created by Dhruv Walia

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

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< Height of Tetrahedron Calculators

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LaTeX Go Height of Tetrahedron = sqrt((8*Face Area of Tetrahedron)/(3*sqrt(3)))

Height of Tetrahedron

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

Height of Tetrahedron given Circumsphere Radius

LaTeX Go Height of Tetrahedron = 4/3*Circumsphere Radius of Tetrahedron

Height of Tetrahedron given Insphere Radius

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

Height of Tetrahedron given Midsphere Radius Formula

LaTeX Go

Height of Tetrahedron = 2*sqrt(4/3)*Midsphere Radius of Tetrahedron
h = 2*sqrt(4/3)*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 Height of Tetrahedron given Midsphere Radius?

Height of Tetrahedron given Midsphere Radius calculator uses Height of Tetrahedron = 2*sqrt(4/3)*Midsphere Radius of Tetrahedron to calculate the Height of Tetrahedron, The Height of Tetrahedron given Midsphere Radius formula is defined as the vertical distance from any vertex of the Tetrahedron to the face which is directly opposite to that vertex, and calculated using the midsphere radius of the Tetrahedron. Height of Tetrahedron is denoted by h symbol.

How to calculate Height of Tetrahedron given Midsphere Radius using this online calculator? To use this online calculator for Height of Tetrahedron given Midsphere Radius, enter Midsphere Radius of Tetrahedron (r_m) and hit the calculate button. Here is how the Height of Tetrahedron given Midsphere Radius calculation can be explained with given input values -> 9.237604 = 2*sqrt(4/3)*4.

FAQ

What is Height of Tetrahedron given Midsphere Radius?

The Height of Tetrahedron given Midsphere Radius formula is defined as the vertical distance from any vertex of the Tetrahedron to the face which is directly opposite to that vertex, and calculated using the midsphere radius of the Tetrahedron and is represented as h = 2*sqrt(4/3)*r_m or Height of Tetrahedron = 2*sqrt(4/3)*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 Height of Tetrahedron given Midsphere Radius?

The Height of Tetrahedron given Midsphere Radius formula is defined as the vertical distance from any vertex of the Tetrahedron to the face which is directly opposite to that vertex, and calculated using the midsphere radius of the Tetrahedron is calculated using Height of Tetrahedron = 2*sqrt(4/3)*Midsphere Radius of Tetrahedron. To calculate Height 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 Height of Tetrahedron?

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

Height of Tetrahedron = sqrt(2/3)*Edge Length of Tetrahedron
Height of Tetrahedron = 4/3*Circumsphere Radius of Tetrahedron
Height of Tetrahedron = sqrt((8*Face Area of Tetrahedron)/(3*sqrt(3)))

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