Height of Tetrahedron given Insphere Radius Calculator

✖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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✖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 Insphere Radius [h]

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Height of Tetrahedron given Insphere Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of Tetrahedron = 4*Insphere Radius of Tetrahedron
h = 4*r_i
This formula uses 2 Variables

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.
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.

STEP 1: Convert Input(s) to Base Unit

Insphere Radius of Tetrahedron: 2 Meter --> 2 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = 4*r_i --> 4*2

Evaluating ... ...

h = 8

STEP 3: Convert Result to Output's Unit

8 Meter --> No Conversion Required

FINAL ANSWER

8 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

Height of Tetrahedron given Face Area

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 Insphere Radius Formula

LaTeX Go

Height of Tetrahedron = 4*Insphere Radius of Tetrahedron
h = 4*r_i

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 Insphere Radius?

Height of Tetrahedron given Insphere Radius calculator uses Height of Tetrahedron = 4*Insphere Radius of Tetrahedron to calculate the Height of Tetrahedron, The Height of Tetrahedron given Insphere 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 insphere radius of the Tetrahedron. Height of Tetrahedron is denoted by h symbol.

How to calculate Height of Tetrahedron given Insphere Radius using this online calculator? To use this online calculator for Height of Tetrahedron given Insphere Radius, enter Insphere Radius of Tetrahedron (r_i) and hit the calculate button. Here is how the Height of Tetrahedron given Insphere Radius calculation can be explained with given input values -> 8 = 4*2.

FAQ

What is Height of Tetrahedron given Insphere Radius?

The Height of Tetrahedron given Insphere 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 insphere radius of the Tetrahedron and is represented as h = 4*r_i or Height of Tetrahedron = 4*Insphere Radius of Tetrahedron. 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.

How to calculate Height of Tetrahedron given Insphere Radius?

The Height of Tetrahedron given Insphere 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 insphere radius of the Tetrahedron is calculated using Height of Tetrahedron = 4*Insphere Radius of Tetrahedron. To calculate Height of Tetrahedron given Insphere Radius, you need Insphere Radius of Tetrahedron (r_i). With our tool, you need to enter the respective value for Insphere 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 Insphere 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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