Midsphere Radius of Tetrahedron given Height Solution

STEP 0: Pre-Calculation Summary
Formula Used
Midsphere Radius of Tetrahedron = sqrt(3/2)*Height of Tetrahedron/(2*sqrt(2))
rm = sqrt(3/2)*h/(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.
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.
STEP 1: Convert Input(s) to Base Unit
Height of Tetrahedron: 8 Meter --> 8 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rm = sqrt(3/2)*h/(2*sqrt(2)) --> sqrt(3/2)*8/(2*sqrt(2))
Evaluating ... ...
rm = 3.46410161513775
STEP 3: Convert Result to Output's Unit
3.46410161513775 Meter --> No Conversion Required
FINAL ANSWER
3.46410161513775 3.464102 Meter <-- Midsphere Radius of Tetrahedron
(Calculation completed in 00.020 seconds)

Credits

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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 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 Height Formula

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

Midsphere Radius of Tetrahedron given Height calculator uses Midsphere Radius of Tetrahedron = sqrt(3/2)*Height of Tetrahedron/(2*sqrt(2)) to calculate the Midsphere Radius of Tetrahedron, The Midsphere Radius of Tetrahedron given Height 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 height of Tetrahedron. Midsphere Radius of Tetrahedron is denoted by rm symbol.

How to calculate Midsphere Radius of Tetrahedron given Height using this online calculator? To use this online calculator for Midsphere Radius of Tetrahedron given Height, enter Height of Tetrahedron (h) and hit the calculate button. Here is how the Midsphere Radius of Tetrahedron given Height calculation can be explained with given input values -> 3.464102 = sqrt(3/2)*8/(2*sqrt(2)).

FAQ

What is Midsphere Radius of Tetrahedron given Height?
The Midsphere Radius of Tetrahedron given Height 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 height of Tetrahedron and is represented as rm = sqrt(3/2)*h/(2*sqrt(2)) or Midsphere Radius of Tetrahedron = sqrt(3/2)*Height of Tetrahedron/(2*sqrt(2)). Height of Tetrahedron is the vertical distance from any vertex of the Tetrahedron to the face which is directly opposite to that vertex.
How to calculate Midsphere Radius of Tetrahedron given Height?
The Midsphere Radius of Tetrahedron given Height 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 height of Tetrahedron is calculated using Midsphere Radius of Tetrahedron = sqrt(3/2)*Height of Tetrahedron/(2*sqrt(2)). To calculate Midsphere Radius of Tetrahedron given Height, you need Height of Tetrahedron (h). With our tool, you need to enter the respective value for Height 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 Height 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 = (3*sqrt(3))/Surface to Volume Ratio of Tetrahedron
  • Midsphere Radius of Tetrahedron = (6*sqrt(2)*Volume of Tetrahedron)^(1/3)/(2*sqrt(2))
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